Haryana Board Class 6 Maths Solutions For Chapter 1 Knowing Our Numbers

Haryana Board Class 6 Maths Solutions For Chapter 1 Knowing Our Numbers

• Numbers help us to count concrete objects.
• Numbers help us to say which collection of objects is bigger and arrange things in order first, second, etc.
• Ascending order: Ascending order means arrangement from the smallest to the greatest.
• Descending order: Descending order means arrangement from the greatest to the smallest.
• 99 is the greatest 2 – digit number.
• The greatest 3 digit number is 999.
• The next number which comes next to 9999 is 10000, is called ten thousand.
• The smallest 7 – digit number is ten lakh.
• The smallest 8 – digit number is one crore.
• 1 crore = 100 lakhs = 10,000 thousands.
• 1 billion = 1000 million
• Number system is backbone to mathematics.
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits. We write all numbers using these 10 digits.
• Zero was invented by an ancient Indian mathematician.
• The term ‘Predecessor’ means the number before a given number. Eg. In the numbers 48, 49, 48 is predecessor.
• The term ‘Successor’ means the number after a given number. Eg. In the number 48, 49, 49 is the successor.
• The value of each digit in a given number depends upon its place value of the number, proceeding from right to left, everytime the place value increases by 10 times.
• To find total number of same digit numbers = Greatest number – Smallest number + 1
• Methods of numeration are commonly of two types, they are
• Indian system of numeration (Hindu – Arabic)
• International system of numeration.
• The method of representing a number in digits or figures is called notation.
• The method of expressing a number in words is called numeration.
• Place value of a digit in a number = Its face value x Position value
• Place value chart of number in Indian system of numerations is given below.

Indian System Place Value Chart Table

• Place value chart of numbers in International system of Numerations is given below.

International system place value chart table

• Comparison of Indian and International system of numeration.

• • Note: 1 lakh = 100 thousands
  • 10 lakhs = 1 million
  • 1 crore = 10 millions
  • 10 crores = 100 millions
  • 100 crores = 1 billion
• To measure water flow we use ‘Cusecs’ and T.M.C.
  • Cusecs = Cubic feet per second
    = Flow of 28.316 litre per second
  • T.M.C = Thousand million cubic feet
    = 283160000000 litres.
• To measure the weights of products we use grams, kilograms, quintal, tonnes …… etc.
  • 1 kg = 1000 grams
  • 1 quintal = 100 kgs
  • 1 tonne = 1000 kgs
• To measure the distances we use mm, cm, m, km ….. etc.
• In order to estimate or round off a number to the nearest
  • a) Tens:
    • If the digit at ones place is less than 5, replace the one’s digit by zero, other digits remain same.
    • If the digit at ones place is greater than or equal to 5, increase tens digit by ‘1’, replace units digit by ‘0’. Other digits remain same.
  • b) Hundreds:
    • Observe the digit at tens place. If it is less than 5, then hundreds place remains same. Put zeroes in tens and units places.
    • If the digit at tens place is greater than or equal to 5 then add ‘1’ to hundreds place. Put zeroes in tens and units places.
• Observe the following table and fill with the appropriate numbers in the table and write in words.

Haryana Board Class 6 Maths Knowing Our Numbers Solutions

Question 1. Can you instantly find the greatest and the smallest numbers in each row?

1. 382, 4972, 18, 59785, 750.

Solution. Greatest number is 59785.

Smallest number is 18.

2. 1473, 89423, 100, 5000, 310.

Solution. Greatest number is 89423.

Smallest number is 100.

3. 1834, 75284, 111, 2333, 450

Solution. Greatest number is 75284.

Smallest number 111.

4. 2853, 7691, 9999, 12002, 124

Solution. Greatest number is 12002.

Smallest number is 124.

Was that easy? Why was it easy?

Solution. Yes! it was easy. We just looked at the number of digits and found the answer. The greatest number has the most thousands and smallest is only in hundreds or in tens.

Question 2. Find the greatest and the smallest numbers.

1. 4536, 4892, 4370, 4452

Solution. Greatest number is 4892;

Smallest number is 4370.

2. 15623, 15073, 15189, 15800

Solution. Greatest number is 15800;

Smallest number is 15073.

3. 25286, 25245, 25270, 25210

Solution. Greatest number is 25286;

Smallest number is 25210.

4. 6895, 23787, 24569, 24659

Solution. Greatest number is 24659;

Smallest number is 6895.

Place Value And Face Value Explained Class 6 HBSE

Question 3. Use the given digits without repetition and make the greatest and smallest 4-digit numbers (Hint: 0754 is a 3-digit number.)

a. 2, 8, 7, 4

Solution. Greatest four digit number = 8742;

Smallest four digit number = 2478.

b. 9,7,4,1

Solution. Greatest four digit number = 9741;

Smallest four digit number = 1479.

c. 4, 7, 5,0

Solution. Greatest four digit number = 7540;

Smallest four digit number = 4057.

d. 1,7,6,2

Solution. Greatest four digit number = 7621;

Smallest four digit number = 1267.

e. 5, 4, 0,3

Solution. Greatest four digit number = 5430;

Smallest four digit number = 3045.

Question 4. Now make the greatest and smallest 4-digit numbers by using any one digit twice. (Hint: Think in each case which digit will you use twice.)

a. 3,8,7

Solution. Greatest four digit number=8873;

Smallest four digit number = 3378.

b. 9,0,5

Solution. Greatest four digit number = 9950;

Smallest four digit number = 5009.

c. 0,4,9

Solution. Greatest four digit number = 9940;

Smallest four digit number = 4009.

d. 8,5,1

Solution. Greatest four digit number = 8851;

Smallest four digit number = 1158.

Rounding Off Numbers Class 6 Haryana Board

Question 5. Take two digits, say 2 and 3. Make 4-digit numbers using both the digits equal number of times.

Which is the greatest number?

Which is the smallest number?

How many different numbers can you make in all ?

Solution. Four digit numbers formed by using two digits 2 and 3 equal number of times are given below:

2233, 2323, 2332, 3223, 3232, 3322

The largest number is 3322

The smallest number is 2233

We can make in all 6 different numbers.

Question 6. Think of five more situations where you compare three or more quantities.

1. Comparing your marks to others
2. Comparing weight of two wrestlers
3. Comparing your height to other’s
4. Comparing the distance and the displacement.,
5. Comparing prices in the shop and on amazon.

Question 7. Arrange the following numbers in ascending order:

a. 847, 9754, 8320, 571

Solution. 571, 847, 8320, 9754

b. 9801, 25751, 36501, 38802

Solution. 9801, 25751, 36501, 38802

Question 8. Arrange the following numbers in descending order:

a. 5000, 7500, 85400, 7861

Solution. 85400, 7861, 7500, 5000

b. 1971, 45321, 88715, 92547

Solution. 92547, 88715, 45321, 1971

Question 9. Make ten such examples of ascending / descending order and solve them.

Question 1. 331, 198, 4403, 1311

Solution. Ascending Order: 198, 331, 1311, 4403

Descending Order: 4403, 1311, 331, 198

Question 2. 4314, 85222, 13, 4000

Solution. Ascending Order: 13, 4000, 4314, 85222

Descending Order: 85222, 4314, 4000, 13

Question 3. 144, 8520, 3381, 4018

Solution. Ascending Order: 144, 3381, 4018, 8520

Descending Order: 8520, 4018, 3381, 144

Roman Numerals Class 6 HBSE Maths

Question 4. 33, 980, 11384, 99

Solution. Ascending Order: 33, 99, 980, 11384

Descending Order: 11384, 980, 99, 33

Question 5. 304, 1405, 331, 84

Solution. Ascending Order :84, 304, 331, 1405

Descending Order : 1405, 331, 304, 84

Question 6. 247, 1578, 76, 14215

Solution. Ascending Order: 76, 247, 1578, 14215

Descending Order : 14215, 1578, 247, 76

Question 7. 1321, 618, 53, 12125

Solution. Ascending Order: 53, 618, 1321, 12125

Descending Order: 12125, 1321, 618, 53

Question 8. 7328, 14206, 48, 665

Solution. Ascending Order: 48, 665, 7328, 14206

Descending Order: 14206, 7328, 665, 48

Question 9. 536, 88, 11215, 7325

Solution. Ascending Order : 88, 536, 7325, 11215

Descending Order : 11215, 7325, 536, 88

Question 10. 228, 36, 10116, 3426

Solution. Ascending Order :36, 228, 3426, 10116

Descending Order: 10116, 3426, 228, 36

Question 10. Read and expand the numbers wherever there are blanks.

Write five more 5-digit numbers, read them and expand them.

Solution.

Question 11. Read and expand the numbers wherever there are blanks.

Solution.

Question 12. What is 10 – 1 = ?

Solution. 10 – 1 = 9

Question 13. What is 100 – 1 = ?

Solution. 100 – 199

Question 14. What is 10,000 – 1 = ?

Solution. 10,000 – 19,999

Question 15. What is 1,00,000 – 1 = ?

Solution. 1,00,000 – 199,999

Question 16. What is 1,00,00,000 – 1 = ?

Solution. 1,00,00,000 – 1 = 99,99,999

Question 17. Give five examples where the number of things counted would be more than 6-digit number.

Solution.

1. Number of people in our contry.
2. Number of copies of Ramayana published each year.
3. Number of grains in a sack full of wheat.
4. Number of railway tickets sold in a day at Railway Stations in Capital of India.
5. Number of saving account holders in Nationalised bank in a region.

Question 18. Starting from the greatest 6-digit number, write the previous five numbers in descending order.

Solution. The largest 6-digit number is 9,99,999. The next 5 numbers are:

10,00,000, 10,00,001, 10,00,002, 10,00,003, 10,00,004

In descending order, the next 5 numbers are:

10,00,004, 10,00,003 10,00,002, 10,00,001, 10,00,000

Question 19. Starting from the smallest 8-digit number, write the next five numbers in ascending order and read them.

Solution. The smallest 8-digit number is 1,00,00,000. The next 5 numbers in ascending order are:

1,00,00,001 one crore and one

1,00,00,002 one crore and two

1,00,00,003 one crore and three

1,00,00,004 one crore and four

1,00,00,005 one crore and five

Question 20. Read these numbers. Write them using placement boxes and then write expanded forms.

1)475320

2) 9847215

3) 97645310

4) 30458094

a) Which is the smallest number?

b) Which is the greatest number?

c) Arrange these numbers in ascending and descending orders?

Solution.

a) The smallest number is 475320

b) The greatest number is 97645310

c) The numbers in ascending order as follows 475320, 9847215, 30458094, 97645310.

The numbers in descending order are as follows: 97645310, 30458094, 9847215, 475320

Question 21. Read these numbers.

1) 527864

2) 95432

3) 18950049

4) 70002509

a) Write these numbers using placement boxes and then using commas in Indian as well as International system of numeration.

b) Arrange these in ascending and descending order.

Solution. a) 1. Using placement boxes:

2. Using commas:

Number             Number using commas

1) 527864             5,27,864
2) 95432               95,432
3) 18950049         1,89,50,049
4) 70002509         7,00,02,509

b) In ascending order, the numbers are 95432, 527864, 18950049, 70002509.

In descending order, the numbers are 18950049, 70002509, 527864, 95432.

Question 22. You have the following digits 4, 5, 6, 0, 7 and 8. Using them, make five numbers each with 6-digits.

a) Put commas for easy reading.

b) Arrange them in ascending and descending order.

Solution. The 5 numbers each with 6 digits using the digits 4, 5, 6, 0, 7 and 8 may be as given below.

876540

867540

876450

876045

867405

a) The above numbers putting commas are as given below.

8,76,540

8,67,540

8,76,450

8,76,045

8,67,405

b) The above numbers arranged in ascending order are as follows:

8,67,405

8,67,540

8,76,045

8,76,450

8,76,540

The above numbers arranged in descending order are as follows:

8,76,540

8,76,450

8,76,045

8,67,540

8,67,405

Question 23. Take the digits 4, 5, 6, 7, 8 and 9. Make any three numbers each with 8 digits. Put commas for easy reading.

Solution. The required numbers may be taken as given below.

9,88,77,456, 9,88,77,465, 9,88,77,654

Question 24. From the digits 3, 0 and 4 make five numbers each with 6 digits. Use commas.

Solution. The required numbers may be taken as given below.

3,00,343, 4,03,403, 4,44,330, 3,43,340, 4,40,340

Chapter 1 Knowing Our Numbers Exercise 1.1

Question 1. Fill in the blanks:

a) 1 lakh = …………………. ten thousand.

b) 1 million = ………………… hundred thousand.

c) 1 crore = …… ten lakh.

d) 1 crore = ……………….. million.

e) 1 million = ……………lakh.

Solution. a) 1 lakh = 10 ten thousand.

b) 1 million = 10 hundred thousand.

c) 1 crore = 10 ten lakh.

d) 1 crore = 10 million.

e) 1 million = 10 lakh.

Question 2. Place commas correctly and write the numerals:

a) Seventy three lakh seventy five thousand three hundred seven.

Solution. 73,75,307.

b) Nine crore five lakh forty one.

Solution. 9,05,00,041.

c) Seven crore fifty two lakh twenty one thousand three hundred two.

Solution. 7,52,21,302.

d) Fifty eight million four hundred twenty three thousand two hundred two.

Solution. 58,423,202.

e) Twenty three lakh thirty thousand ten.

Solution. 23,30,010.

Question 3. Insert commas suitably and write the names accroding to Indian System of Numeration:

a) 87595762

b) 8546283

c) 99900046

d) 98432701

Solution. a) 8,75,95,762 = Eight crores, seventy five lakhs, ninety five thousand, seven hundred and sixty two.

b) 85,46,283 = Eighty five lakhs, forty six thousand, two hundred and eighty three.

c) 9,99,00,046 = Nine crores, ninety-nine lakhs and forty six.

d) 9, 84, 32,701 = Nine crores, eighty four lakhs, thirty two thousand, seven hundred and one.

Question 4. Insert commas suitable and write the names accroding to international system of numeration:

a) 78921092

b) 7452283

c) 99985102

d) 48049831

Solution. a) 78,921,092 = Seventy eight million, nine hundred twenty one thousand ninety two

b) 7,452,283 = Seven million, four hundred fifty two thousand, two hundred eighty three.

c) 99,985,102 = Ninety nine million, nine hundred eighty five thousand, one hundred two.

d) 48,049,831 = Forty eight million, forty nine thousand, eight hundred thirty one.

Question 5. How many centimetres make a kilometre?

Solution. 1,00,000 centimeters = 1 kilometere.

Question 6. How many milligrams make one kilogram?

Solution. 10,00,000 milligrams = 1 kilogram.

Question 7. A box contains 2,00,000 medicine tablets each weighing 20 mg. What is the total weight of all the tablets in the box in grams and in kilograms?

Solution. Total weight of all the tablets in the box

= 2,00,000 x 20 mg. = 40,00,000 mg

= 4000 g [1g = 1000 mg]

= 4 kg

Question 8. A bus started its journey and reached different places with a speed of 60 km/hr. The journey is shown below.

1) Find the total distance covered by the bus from A to D.

2) Find the total distance covered by the bus from D to G.

3) Find the total distance covered by the bus, if it starts from A and returns back to A.

4) Can you find the difference of distances from C to D and D to E?

5) Find out the time taken by the bus to reach

a) A to B

b) C to D

c) E to G

d) Total journey

Solution. 1) Total distance covered by the bus from A to D

= 4170 km + 3410 km + 2160 km

= 9740 km.

2) Total distance covered by the bus from D to G.

= 8140 km + 4830 km + 2550 km

= 15520 km

3) Total distance covered by the bus

= Distance from A to D + Distance from D to G + Distance from G to A

= 9740 km + 15520 km + 1290 km = 26550 km

4) Distance from C to D = 2160 km

Distance from D to E = 8140 km

∴ Difference of distances from C to D and D to E = 8140 km – 2160 km = 5980 km.

5) a) Time taken by the bus to reach A to B.

= \(\frac{4170}{60} \text { hrs. }=\frac{417}{6} \text { hrs }=69 \frac{3}{6} \text { hrs. }\)

= 69 hrs 30 minutes

b) Time taken by the bus to reach C to D

= \(\frac{2160}{60} \mathrm{hrs}=36 \mathrm{hrs}\)

c) Time taken by the bus to reach E to G.

= \(\frac{4830+2550}{60} \mathrm{hrs}=\frac{7380}{60} \mathrm{hrs} .=123 \mathrm{hrs} .\)

d) Time taken by the bus for total journey

= \(\frac{26550}{60} \mathrm{hrs.}=442 \frac{1}{2} \mathrm{hrs.}\)

= 442 hrs. 30 minutes.

Question 9. Raman’s shop

The sales during the last year

a) Can you find the total weight of apples and oranges Raman sold last year?

Weight of apples: ………. kg

Weight of oranges = ……… kg

Therefore, total weight = ……… kg + ……. kg = …….. kg

Answer – The total weight of oranges and apples = ……. kg.

Solution. Weight of apples sold during the last year = 2457 kg.

Weight of oranges sold during the last year = 3004 kg.

Total weight of apples and oranges Raman sold during the last year.

= 2457 kg + 3004 kg

= 5461 kg.

Use Of Brackets And BODMAS Rule Class 6 HBSE

b) Can you find the total money Raman got by selling apples?

Solution. Total money Raman got by selling apples

= Rs. 2457 x 40

= Rs. 98,280

c) Can you find the total money Raman got by selling apples and oranges together?

Solution. Total money Raman got by selling Oranges

= Rs. 3004 × 30

= Rs. 90,120

∴ Total money Raman got by selling apples and oranges together. = 98,280 + 90, 120 = Rs. 1,88,400

d) Make a table showing how much money Raman received from selling each item. Arrange the entries of amount of money received in descending order. Find the item which brought him the highest amount. How much is this amount?

Solution.

The entries of amount of money received in descending order are as follows. Rs. 2,53,670, Rs. 2,40,012, Rs. 1,60,040, Rs. 98,280, Rs. 90,120, Rs. 68,280, Rs. 38,350 The items which bought him the highest amount is tooth brushes. This highest amount is Rs. 2,53,670.

Chapter 1 Knowing Our Numbers Exercise 1.2

Question 1. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

Solution. Number of tickets sold on the first day = 1094

Number of tickets sold on the second day = 1812

Number of tickets sold on the third day = 2050

Number of tickets sold on the final day = 2751

∴ Total number of tickets sold on all the four days 1094 + 1812 + 2050 + 2751 = 7707

Question 2. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?

Solution. Runs scored so far = 6,980

Runs wished to be scored = 10,000

∴ Runs needed more = 10,000 – 6,980 = 3,020

Question 3. In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?

Solution. Votes registered by the successful candidate = 5,77,500

Votes secured by the nearest rival = 3,48,700

Margin by which the successful candidate won the election = 5,77,500 – 3,48,700 = 2,28,800

Question 4. Kirti bookstore sold books worth Rs. 2,85,891 in the first week of June, books worth Rs. 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Solution. Sale of the books in the first week = Rs. 2,85,891

Sale of books in the second week = Rs. 4,00,768

The sale was greater in the second week by

= Rs. 4,00,768 – Rs. 2,85,891

= Rs. 1,14,877

Question 5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.

Solution. Greatest number that can be written using the digits 6, 2, 7, 4, 3 each only once = 76,432.

Least number that can be written using the digits 6, 2, 7, 4, 3 each only once = 23,467.

∴ Difference between the greatest and least numbers that can be written using the digits 6, 2, 7, 4, 3 each only once = 76,432 – 23,467 = 52,965

Question 6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006 ?

Solution. Number of screws manufactured by the machine a day on an average = 2,825

Number of days in the month of January, 2006 = 31

∴ Number of screws produced by the machine in the month of January, 2006

= 2,825 x 3187,575.

Question 7. A merchant had Rs. 78,592 with her. She placed an order for purchasing 40 radio sets at Rs. 1200 each. How much money will remain with her after the purchase?

Solution. Money which the merchant had = Rs. 78,592

Cost of 40 radio sets = Rs. 1200 x 40 = Rs. 48,000.

∴ Money that will remain with the merchant after the purchase.

= Rs. 78,592 – Rs. 48,000

= Rs. 30,592.

Question 8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?

(Hint: Do you need to do both the multiplications?)

Solution. Wrong answer = 7236 x 65 = 4,70,340

Correct answer = 7236 × 56 = 4,05,216

∴ Wrong answer was greater than the correct answer by = 4,70,340, – 4,05,216

= 65,124

Question 9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain ?

(Hint: Convert data in cm.)

Solution. 2 m 15 cm = 2 x 100 cm + 15 cm

= 200 cm + 15 cm = 215 cm

40 m = 40 x 100 cm

= 4000 cm

No. of shirts that can be stitched = \(\frac{4000}{215}\) = 18 (approx)

∴ 18 shirts can be stitched and 130 cm cloth will remain.

Question 10. Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg ?

Solution. 4 kg 500 g = 4 × 1000 g + 500 g

= 4000g + 500g = 4500 g.

800 kg = 800 x 1000 g = 800000 g.

Number of boxes loaded = \(\frac{800000}{4500}\) = 178

∴ 178 such boxes can be loaded. (Approximately)

Question 11. The distance between the school and the house of a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.

Solution. 1 km 875 m = 1 x 1000 m +875 m

= 1000 m + 875 m

= 1875 m

Distance covered by her in a day in walking both ways between school and home.

= 1875 x 2 m

= 3750 m

∴ Total distance covered by her in six days. = 3750 x 6m

3 km 750 m × 6

= 22 km 500 m

∴ Distance covered in 6 days = 22 km 500 m.

Question 12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?

Solution. 4 litres and 500 ml = 4500 ml. (∴ 1 litre = 1000 ml.)

Capacity of each glass = 25 ml

No. of glasses it can fill = \(\frac{4500}{25}\) = 180

∴ It can be distributed in 180 glasses.

Chapter 1 Knowing Our Numbers Very Short Answer Questions

Question 1. Write the numbers in ascending (increasing) order:

1) 375, 1475, 15951, 4713

Solution. 375, 1,475, 15,951, 4,713

Comparing the digits in thousands place 1, 15, 4

15 is the greatest; 1 is the smallest

Increasing order is 1, 4, 15.

∴ Ascending order: 375, 1475, 4713, 15951

2) 9,347; 19,035; 22,570; 12,300

Solution. 9,347; 19,035; 22,570; 12,300

Comparing the digits in thousands place 9, 19, 22, 12.

Increasing order of these digits – 9, 12, 19, 22.

∴ Ascending order: 9347, 12300, 19035, 22570.

Question 2. Write the numbers in descending (decreasing) order:

1) 1876, 89715, 45321, 89254

Solution. 1,876; 89,715; 45,321; 89,254

Comparing the digits in thousands place 1, 89, 45, 89.

Descending order: 89, 89, 45, 1

In 89,715 and 89,254 the thousands place 89 is same.

Now compare the digit in hundreds place.

Hundreds place digits are 7, 2.

2 is the smallest and 7 is the greatest.

∴ Descending order: 89,715; 89,254; 45,321; 1,876.

Difference Between Indian And International Number System

2) 3000, 8700, 3900, 18500.

Solution. 3,000; 8,700; 3,900; 18,500

Comparing the digits in thousands place 3, 8, 3, 18.

Descending order: 18,8,3,3 In 3000 and 3900, the thousands place 3 is same.

Now compare the digit in hundreds place.

Hundreds place digits are 0, 9. 0 is the smallest and 9 is the greatest.

Descending order: 18,500; 8,700; 3,900; 3,000.

Question 3. Write the numbers in words:

1) 72,642 = Seventy two thousand six hundred and forty two.

2) 55,345 = Fifty five thousand three hundred and forty five.

3) 66,600 = Sixty six thousand six hundred

4) 30,301 = Thirty thousand three hundred and one.

Question 4. Write the numbers in figures:

1) Forty thousand two hundred seventy – 40,270

2) Fourteen thousand sixty four – 14,064

3) Nine thousand seven hundred – 9,700

4) Sixty thousand – 60,000

Question 5. Write the numbers.

1) The smallest four digit number?

1,000

2) The greatest four digit number?

9,999

3) The smallest five digit number?

10,000

4) The greatest five digit number?

99.999

Question 6. Write the numbers in short form:

1) 3000 + 400 + 7 = 3407

2) 10000 + 2000 + 300 + 50 + 1 = 12351

3) 30000 + 500 + 20 + 5 = 30525

4) 90000 + 9000 + 900 + 90 + 9 = 99999

Question 7. Write the number in figures:

1) Four lakh fifty seven thousand four hundred.

2) Sixty lakh two thousand seven hundred seventy five.

3) Two crore fifty lakh forty thousand three hundred and three.

4) Sixty crore sixty lakh sixty thousand six hundred.

Solution. 1) 4,57,400

2) 60,02,775

3) 2,50,40,303

4) 60,60,60,600

Question 8. Write the expanded form of the number 315645.

Solution. 3,15,645 = 3 x 1,00,000 + 1 x 10,000 + 5 x 1,000 + 6 x 100 + 4 x 10 + 5 x 1

= 3,00,000 + 10,000 + 5,000 + 600 + 40 + 5

Question 9. Write the numbers 67456, 76547, 15476, 75460 in ascending and descending orders

Solution. Ascending order: 15476, 67456, 75460, 76547

Descending order: 76547, 75460, 67456, 15476

Question 10. Insert commas to separate periods and write the number 8555016916 in words in International system.

Solution. 8,555,016,916: Eight billion five hundred fifty five million sixteen thousand nine hundred and sixteen.

Question 11. Write the number 9030608878 in expanded form in International system.

Solution. Put commas for each period then the given number can be written as 9,030,608,878

9,030,608,878 = 9 x 1,000,000,000 + 3 x 10,000,000 + 6 × 100,000 + 0 x 10,000 + 8 x 1,000 + 8 x 100 + 7 × 10 + 8 × 1

Chapter 1 Knowing Our Numbers Short Answer Questions

Question 1. Write the expanded forms of the numbers:

1) 4348 = 4 x 1000 + 3 x 100 + 4 × 10 + 8 × 1

= 4000 + 300 + 40 + 8

2) 30214 = 3 x 10000+0x1000+2×100 + 1×10 +4×1

= 30000 + 200 + 10 + 4

3) 22222 = 2 × 10000 + 2 × 1000 + 2 x 100 + 2 × 10 + 2 × 1

= 20000 + 2000 + 200 + 20 + 2

4) 75025 = 7 x 10000 + 5 x 1000 + 0 x 100 + 2 x 10 + 5 x 1

= 70000 + 5000 + 20 + 5

Question 2. Write the smallest and greatest of all two digit, three digit, four digit, five digit, six digit, seven digit, eight digit numbers.

Solution.

Question 3. Write these numbers in words:

1) 12,36,99,140 – Twelve crores thirty six lakhs ninety nine thousand one hundred and forty.

2) 2,50,00,350 – Two crores fifty lakhs three hundred and fifty.

Question 4. Write the numbers using commas:

1) 11245670

2) 22402151

3) 30608712

4) 190308020

Solution. Using commas:

1) 1,12,45,670

2) 2,24,02,151

3) 3,06,08,712

4) 19,03,08,020

Question 5. Write the numbers in words:

1) 34,025

2) 7,09,115

3) 47,60,00,317

4) 6,18,07,000

Solution. 1) 34,025 = Thirty four thousand and twenty five.

2) 7,09,115 = Seven lakh nine thousand one hundred and fifteen.

3) 47,60,00,317 = Forty seven crore sixty lakh three hundred and seventeen.

4) 6,18,07,000 = Six crore eighteen lakh and seven thousand

Question 6. Write the numbers in expanded form:

1) 6,40,156

2) 63,20,500

3) 1,25,30,275

4) 75,80,19,202

Solution. 1) 6,40,156 = 6 × 1,00,000 + 4 x 10,000 + 0 x 1000 + 1 x 100 + 5 × 10 + 6 × 1

= 6,00,000 + 40,000 + 100 + 50 + 6

2) 63,20,500 = 6 x 10,00,000 + 3 x 1,00,000 + 2 x 10,000 + 0 x 1,000 + 5 × 100 + 0 × 10 + 0 × 1

= 60,00,000 + 3,00,000 + 20,000 + 500

3) 1,25,30,275 = 1 × 1,00,00,000 + 2 x 10,00,000 + 5 × 1,00,000 + 3 x 10,000 + 0 × 1,000 + 2 x 100 + 7 × 10 + 5 × 1

= 1,00,00,000 + 20,00,000 + 5,00,000 + 30,000 + 200 + 70 + 5

4) 75,80,19,202 = 7 × 10,00,00,000 + 5 x 1,00,00,000 + 8 x 10,00,000 + 0x 1,00,000 + 1 × 10,000 + 9 × 1,000 + 2 x 100 + 0 × 10 + 2 × 1.

= 70,00,00,000 + 5,00,00,000 + 80,00,000 + 10,000 + 9,000 + 200 + 2

Question 7. Write the following numbers in short form (Standard notation):

1) 50,00,000 + 4,00,000 + 20,000 + 8,000 + 500 + 20 + 4.

Solution. 54,28,524

2) 6,00,00,000 + 40,00,000 + 3,00,000 + 20,000 + 500 + 1.

Solution. 6, 43, 20, 501

3) 3,00,00,000 + 3,00,000 + 7,000 + 800 + 80 + 1.

Solution. 3, 03, 07, 881

4) 7,00,00,000 + 70,00,000 + 7,000 + 70

Solution. 7,70, 07, 070

Question 8. Write the greatest and smallest number formed by the digits 5, 3, 4, 0 and 7 and find their difference.

Solution. Greatest Number = 75430

Smallest Number = 03457

Difference = 71973

Note: In the problem they didn’t mention the difference between five digit numbers.

Question 9. Write the expanded form of the numbers:

1) 64

2) 325

3) 5078

4) 29500

Solution. 1) 64 = 6 × 10 + 4 × 1

= 60 + 4

2) 325 = 3 x 100 + 2 x 10 + 5 × 1

= 300 + 20 + 5

3) 5078 = 5 × 1000 + 0 x 100 + 7 x 10 + 8 x 1

= 5000 + 70 + 8

4) 29500 = 2 x 10,000 + 9 × 1,000 + 5 x 100 + 0 × 10 + 0 x 1

= 20,000 + 9,000 + 500

Question 10. How many millilitres will make a 1 kilolitre ?

Solution. 1 kilolitre = 1000 litres

= 1000 × 100 centilitres

= 1000 x 100 x 10 millilitres

1 kilolitre = 10,00,000 millilitres

Chapter 1 Knowing Our Numbers Long Answer Questions

Question 1. Write any ten numbers with digits 5 in crores, 2 in lakhs 1 in ten thousands, 6 in tens, 3 in ones place.

Solution. Ten numbers are

5,02, 10,063

5, 32, 16, 463

5, 42, 17,863

5,72, 19, 463

5,92, 12, 763

15, 82, 18, 563

25, 62, 13, 963

5, 22, 15, 663

5, 52, 14, 363

5, 12, 11, 263

Question 2. A box contains 1,00,000 Tablets (medicine) each weighing 20 mg. What is the weight of all the tablets in the box in both grams and kilograms?

Solution. Weight of each tablet = 20 mg

No. of tablets in the box = 1,00,000

∴ Weight of all the tablets in the box = 20 × 1,00,000

= 20,00,000 mg

1kg = 10,00,000 mg

20,00,000 mg = 2 x 10,00,000

= 2 x 1 kg = 2 kg

1 kg = 1000 gms

2 kg = 2 x 1000 = 2000 gms

Question 3. A petrol tanker contain 20,000 litres of petrol. Express the quantity of petrol in kilolitres and millilitres.

Solution. Quantity of petrol in the Tanker = 20,000 litres

1000 litres = 1 kilolitres

20,000 litres 20 x 1000 = 20 x 1 kilolitres

= 20 kilolitres

1 kilolitre = 10,00,000 millilitres

20 kilolitres = 20 × 10,00,000

= 2,00,00,000 millilitres

Class 6 HBSE Maths Chapter 1 Important Questions

Question 4. The cloth required to make a shirt of school uniform for each boy is 1 m 80 cm. How many shirts can tailor stitch using 40 m of cloth ? How much cloth will be left ?

Solution. Cloth required to make a shirt of school uniform for each boy = 1 m 80 cm

= 100 + 80 = 180 cm

Total length of the cloth = 40 m

= 40 x 100 4000 cm

No. of shirts stitched = \(\frac{4000}{180}\)

= 22

Length of the cloth left = 40 cm

Question 5. A hotel has 15 litres milk. 25 ml of milk is required to prepare a cup of tea. How many cups of tea can be made with the milk?

Solution. Quantity of milk in the hotel = 15 litres

= 15 × 1000

= 15000 ml

Milk required to prepare a cup of tea = 25 ml

Number of cups of tea that can be made with the milk = 15000 ÷ 25

= 600

Question 6. Write the following numbers in words in both Indian and International systems.

1) 6756327

Solution.

Indian system:

67,56,327 = Sixty seven lakhs fifty six thousand three hundred and twenty seven.

International system:

6,756, 327 = Six million seven hundred fifty six thousand three hundred and twenty seven.

2) 45607087

Solution.

Indian system:

4,56,07,087 = Four crore fifty six lakh seven thousand eighty seven.

International system:

45,607,087 = Forty five million six hundred seven thousand and eighty seven.

3) 8560707236

Solution.

Indian system:

856,07,07,236 = Eight hundred fifty six crore seven lakhs seven thousand two hundred and thirty six.

International system:

8,560,707,236 = Eight billion five hundred sixty million seven hundred seven thousand two hundred and thirty six.

Question 7. Write some daily life situations where we can use large numbers.

Solution.

1. To find out the distance between the Sun and the Earth.
2. To calculate the population of India.
3. The number of stars in the Universe.
4. The number of cells in the human body.
5. To find out the mass of earth.

Question 8. A box of medicine tablets contains 3,00,000 tablets each weighing 15mg. What is the total weight of all the tablets in the box in grams and in kilograms?

Solution. Number of tablets in the box = 3,00,000

Weight of each tablet = 15 mg

Total weight of the box = 3,00,000 x 15

= 45,00,000 mg

Total weight of the box in grams = \(\frac{4500000}{1000}\)

[∴ 1 gm = 1000 mg 1 mg = \(\frac{1}{1000}\) gr]

= 4500 grams.

The total weight of the box in kilograms = \(\frac{4500}{1000}\)

[∴ 1kg = 1000 gr 1 gr = \(\frac{1}{1000}\)kg]

= 4.5 kg

Question 9. Damodhar wants to buy onions in Kurnool market. Each onion bag’s weight is 45 kg. He loaded 326 onion bags with 45kg in a lorry. Find the total weight of onions in kilograms and quintals?

Solution. No. of onion bags that Damodhar loaded = 326 onion bags

The weight of each onion bag = 45 kg

The weight of 326 onion bags = 326 × 45

= 14670 kg

∴ The total weight of onions in kilograms = 14670 kg

∴ The total weight of onions in quintals = \(\frac{14670}{100}\)

[∴ 1 quintal = 100 kg 1 kg = \(\frac{1}{100}\)]

= 146.7 quintal

Chapter 1 Knowing Our Numbers Objective Type Questions

Choose the correct answer :

Question 1. The smallest five digit number

1. 1000
2. 9999
3. 10000
4. 99999

Answer. 3. 10000

Question 2. Place value of 2 in 632587

1. Lakhs
2. Tens
3. Hundreds
4. Thousands

Answer. 4. Thousands

Question 3. ‘Sixty lakhs six’ write in figures

1. 600006
2. 6000006
3. 660000
4. 60006

Answer. 2. 660000

Question 4. Round off 220 to their nearest hundred

1. 300
2. 200
3. 100
4. 400

Answer. 2. 200

Question 5. Number of digits in one crore

1. 7
2. 8
3. 9
4. 6

Answer. 2. 8

Question 6. 1 crore = ….. lakhs

1. 1000
2. 10
3. 100
4. \(\frac{1}{10}\)

Answer. 3. 100

Question 7. 1 lakh = ……. hundreds

1. 1000
2. 100
3. 10
4. 10000

Answer. 1. 1000

Question 8. 10 lakhs = ….. millions

1. 1
2. 10
3. 100
4. 1000

Answer. 1. 1

Question 9. 1 billion = ….. crores

1. 10
2. 100
3. 1000
4. 10000

Answer. 2. 100

Question 10. 302179468 the digit in the Ten millions place is

1. 1
2. 2
3. 0
4. 3

Answer. 3. 0

Question 11. 1 kg = …. gms

1. 10
2. 100
3. 10000
4. 1000

Answer. 4. 1000

Question 12. Quantity of oil in tankers, water in reservoirs are marked with

1. litres
2. millilitres
3. kilolitres
4. centilitres

Answer. 3. kilolitres

Question 13. How many thousands make a million?

1. 100
2. 1000
3. 10
4. 10000

Answer. 2. 1000

Question 14. Which of the 34895, 348891, 34899, 34893 number is smallest?

1. 34895
2. 34891
3. 34899
4. 34893

Answer. 2. 34891

Question 15. The number system which we use in our daily use

1. American
2. French
3. British
4. Hindu Arabic

Answer. 4. Hindu Arabic

Question 16. Number for “Seventy thousand six hundred and eight”

1. 70608
2. 706008
3. 70068
4. 70000608

Answer. 1. 70608

Question 17. Write 22021986 in international system using commas

1. 2,20,21,986
2. 220,21,986
3. 22,021,986
4. 2,202,1986

Answer. 3. 22,021,986

Question 18. Distance covered by a road roller in 1 turn it covers 400 mts. Distance covered by the road roller in 5 turns is

1. 80 mts
2. 200 mts
3. 2000 mts
4. 20000 mts

Answer. 3. 2000 mts

Question 19. 120 litres of milk will be supplied daily to a hotel. If each student is given 250 ml of milk then number of students are.

1. 48
2. 480
3. 24
4. 240

Answer. 2. 480

Question 20. Ascending order means

1. Smallest to greatest
2. Greatest to smallest
3. Both A & B
4. None

Answer. 1. Smallest to greatest

Question 21. Descending order means

1. Smallest to greatest
2. Greatest to smallest
3. Both A & B
4. None

Answer. 2. Greatest to smallest

Question 22. The numerical form of ‘sixty thousand sixty’ is

1. 60,066
2. 66,060
3. 60,060
4. 60606

Answer. 3. 60,060

Question 23. The greatest number formed by the digits 5,0,8,2

1. 5082
2. 8052
3. 8502
4. 8520

Answer. 4. 8520

Question 24. The smallest number formed by the digits 3, 7, 0,8

1. 3708
2. 3078
3. 3780
4. 8730

Answer. 2. 3078

Question 25. How many possible 4 digit numbers can be formed with digits 3, 0, 6, 4.

1. 24
2. 16
3. 18
4. 20

Answer. 3. 18

Question 26. How many possible 4 digit numbers can be formed with digits 2, 8, 3, 7.

1. 24
2. 18
3. 20
4. 26

Answer. 1. 24

Question 27. The greatest 5 digit number

1. 10000
2. 99989
3. 99999
4. 99990

Answer. 3. 99999

Question 28. The smallest 4 digit number

1. 1001
2. 9990
3. 9999
4. 1000

Answer. 4. 1000

Question 29. Who invented zero ?

1. Indians
2. Greeks
3. Romans
4. Italians

Answer. 1. Indians

Question 30. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called

1. Numbers
2. Place values
3. Digits
4. All the above

Answer. 3. Digits

Question 31. Ramanujan’s number

1. 1792
2. 1972
3. 1529
4. 1729

Answer. 4. 1729

Question 32. National Mathematics day

1. Jan 22
2. Dec 22
3. Feb 22
4. Aug 22

Answer. 2. Dec 22

Question 33. Which is the greatest among the following?

1. 67456
2. 76547
3. 15476
4. 75460

Answer. 2. 76547

Question 34. Which is the smallest among the following?

1. 64567
2. 66000
3. 60457
4. 64057

Answer. 3. 60457

Question 35. The ‘Predecessor’ of ‘1000’ is

1. 999
2. 1001
3. 990
4. 1010

Answer. 1. 999

Question 36. The ‘Successor’ of ‘989’ is

1. 988
2. 990
3. 980
4. 1000

Answer. 2. 990

Question 37. The place value of ‘4’ in the number 75460

1. 1000
2. 400
3. 100
4. 4

Answer. 2. 400

Question 38. The face value of ‘3’ in the number 27340

1. 100
2. 300
3. 30
4. 3

Answer. 4. 3

Question 39. How many 3 digit numbers are there in all ?

1. 999
2. 899
3. 900
4. 901

Answer. 3. 900

Question 40. How many thousands make one lakh ?

1. 10
2. 100
3. 1000
4. 10000

Answer. 2. 100

Question 41. 1 million =

1. 10 lakhs
2. 100 thousands
3. 1000 thousands
4. Both A & C

Answer. 4. Both A & C

Question 42. 1 Crore =

1. 1 million
2. 10 millions
3. 100 millions
4. None

Answer. 2. 10 millions

Question 43. 1 billion =

1. 10 crores
2. 100 crores
3. 1000 crores
4. 100 millions

Answer. 2. 100 crores

Question 44. How many millions make one billion?

1. 10
2. 100
3. 1000
4. 10,000

Answer. 3. 1000

Question 45. Which of the following is used to measure water flow?

1. Cusecs
2. T.M.C
3. Both A & B
4. None

Answer. 3. Both A & B

Question 46. 1 quintal =

1. 10 kg
2. 100 kg
3. 1000 kg
4. None

Answer. 2. 100 kg

Question 47. 1 tonne =

1. 10 kg
2. 100 kg
3. 1000 kg
4. 10000 kg

Answer. 3. 1000 kg

Question 48. The numerical form of ten crores ten thousand and ten

1. 10,00,00,010
2. 10,00,10,000
3. 10,00,10,010
4. 10,10,00,010

Answer. 3. 10,00,10,010

Question 49. The difference between the greatest and smallest numbers with the digits 3,0,7

1. 393
2. 403
3. 693
4. 423

Answer. 4. 423

Question 50. Find the sum of greatest and smallest numbers with the digits 3, 8, 0, 5.

1. 8,888
2. 11,588
3. 12,110
4. 11,591

Answer. 2. 11,588

Question 51. Find the difference between face values of ‘3’s of the number 53231 is

1. 0
2. 2,070
3. 3,030
4. 3,200

Answer. 1. 0

Question 52. Find the difference between place values of ‘8’s of the number 38283 is

1. 0
2. 7,920
3. 8,080
4. 79,920

Answer. 2. 7,920

Question 53. The sum of place values of 5’s of the number 2565 is

1. 495
2. 555
3. 505
4. 5005

Answer. 3. 505

Question 54. 1 litre =

1. 10 ml
2. 100 ml
3. 1000 ml
4. 10000 ml

Answer. 3. 1000 ml

Question 55. 1 meter3 =

1. 10 lt
2. 100 lt
3. 1000 lt
4. 10000 lt

Answer. 3. 1000 lt

Question 56. 1 metric ton =

1. 1 kg
2. 10 kg
3. 100 kg
4. 1000 kg

Answer. 4. 1000 kg

Question 57. 1 kilometer =

1. 100 mt
2. 1000 mt
3. 10000 mt
4. 10 mt

Answer. 2. 1000 ml

Question 58. The place value of ‘6’ of the number ‘536248’

1. 6000
2. 600
3. 60
4. 6

Answer. 1. 6000

Question 59. The face value of ‘3’ of the number 45329

1. 300
2. 100
3. 3
4. None

Answer. 3. 3

Question 60. The smallest number formed by the digits 3, 0, 6, 2

1. 2306
2. 2036
3. 2630
4. 6320

Answer. 2. 2036

Question 61. 1 crore =

1. 100 thousands
2. 1000 thousands
3. 1,00,000 thousands
4. 10,000 thousands

Answer. 4. 10,000 thousands

Fill In The Blanks

Fill in the blanks with suitable answer:

Question 62. Largest four digit number ……..

Answer. 9999

Question 63. The least four digit number with 1, 0, 2, 3 is ……

Answer. 1023

Question 64. The difference in the place values of 7 in 1,70,071 is ……..

Answer. 69,930

Question 65. …….. help us in reading and writing or large numbers easily.

Answer. commas

Question 66. 1 crore = …….. million

Answer. 10

Question 67. ……. is a good way of checking answers.

Answer. Estimation

Question 68. Smallest unit of weight is ……

Answer. milligrams

Question 69. Chandrika brought 4 kg 90 g apples, 2 kg 60 g grapes and 5 kg 300 g mangoes from a fruit shop. Total weight of the fruits is ……

Answer. 11 kg 450 g.

Question 70. Write the number 12,076,211 in words in international system ……..

Answer. Twelve millions seventy six thousand two hundred and eleven

Question 71. A train covers 120 km in 1 hour. How much distance it cover in 6 hours? …….

Answer. 720 km

Question 72. ……. are used for counting number of people in a village or a town.

Answer. large numbers

Question 73. In the International system of numeration commas are placed after every digits starting from the right.

Answer. 3

Question 74. The predecessor of 1001 is …..

Answer. 1000

Question 75. Numerical form of “Seventy Eight thousand four hundred and fourteen” is …….

Answer. 78,414

Question 76. 1 kg = ……. grams.

Answer. 1000

Question 77. The greater among the following number is ……

67456; 76547; 15476; 75460

Answer. 76547

Question 78. 100 crores = …….. billion.

Answer. 1

Question 79. Numerical form of “Ten crores ten thousand and ten” is …….

Answer. 10,00,10,010

Question 80. 67,56,326 when expressed in International system is …….

Answer. 6,756,326