Class 7 Maths Chapter 4 Another Peek Beyond the Point worksheet with MCQs, short answer questions, practice questions and extra questions based on Ganita Prakash Part 2 for revision and exam preparation.

Class 7 Maths Chapter 4 Another Peek Beyond the Point Worksheet

Another Peek Beyond the Point

Class 7 Mathematics | Ganita Prakash Part II | Chapter 4

Worksheet: Decimals, Multiplication and Division

Name:

Class:

Date:

Roll No.:

Marks:

Time:

Instructions:

Show your working wherever necessary.
Keep the decimal point carefully in multiplication and division.
Write units in word problems.
Try to solve the questions without using a calculator.
Check your answers before moving to the next question.

Section A: Understanding Decimals

1. Fill in the blanks.

(a) 0.1 is one __________.

(b) 0.01 is one __________.

(d) In 27.53, the digit 5 is in the __________ place.

(e) In 27.53, the digit 3 is in the __________ place.

(f) 0.5 = __________/10.

(g) 0.25 = __________/100.

(h) 3.7 = 3 + __________.

2. Write each decimal as a sum of place-value parts.

(a) 4.26 =

(b) 8.305 =

(d) 0.608 =

3. Convert the following fractions into decimals.

(a) 7/10 =

(b) 43/100 =

(d) 9/100 =

(e) 6/1000 =

4. Convert the following into fractions with denominators 10, 100 or 1000.

(a) 0.7 =

(b) 0.34 =

(d) 2.06 =

Section B: Multiplication of Decimals

5. Multiply.

(a) 4.6 × 3 =

(b) 7.25 × 4 =

(d) 2.35 × 6 =

(e) 1.08 × 7 =

6. Find the products.

(a) 3.2 × 1.5

(b) 4.25 × 2.4

(d) 5.06 × 1.2

7. Use the decimal-place rule.

Given that 324 × 125 = 40500, find:

(a) 3.24 × 1.25 =

(b) 32.4 × 1.25 =

(d) 324 × 1.25 =

8. Without multiplying fully, predict whether the product is greater than or less than both numbers.

(a) 3.5 × 4.2

Prediction:

(b) 0.4 × 0.7

Prediction:

(d) 0.25 × 0.6

Prediction:

9. Find the missing number.

(a) 5 × = 12.5

(b) 10 × = 7.8

(d) 8 × = 0.64

Section C: Multiplication in Daily Life

10.

A notebook costs ₹18.75. Find the cost of 6 notebooks.

11.

A cyclist travels 12.5 km in one hour. How far will the cyclist travel in 4.5 hours at the same speed?

12.

One bottle contains 0.75 litre of juice. How much juice is there in 8 such bottles?

13.

A rectangular mat is 2.5 m long and 1.8 m wide. Find its area.

14.

One packet weighs 0.125 kg. What is the total weight of 16 packets? Give the answer in kilograms.

Section D: Division by 10, 100 and 1000

15. Divide.

(a) 47.5 ÷ 10 =

(b) 47.5 ÷ 100 =

(d) 6.28 ÷ 10 =

(e) 6.28 ÷ 100 =

(f) 6.28 ÷ 1000 =

16. Complete the table.

Number	÷ 10	÷ 100	÷ 1000
18.6
4.25
0.72
35.04

17. Explain the rule.

When a decimal number is divided by 10, 100 or 1000, what happens to the decimal point?

18.

A 5.6 m ribbon is divided into 10 equal pieces. Find the length of each piece.

Section E: Decimal Division

19. Divide using long division.

(a) 144 ÷ 4

(b) 125 ÷ 8

(d) 325 ÷ 8

20. Find the quotient.

(a) 15.6 ÷ 4 =

(b) 8.4 ÷ 6 =

(d) 0.84 ÷ 7 =

(e) 0.96 ÷ 8 =

21. Divide and show the decimal places clearly.

(a) 18.5 ÷ 5

(b) 6.25 ÷ 4

(d) 0.75 ÷ 5

22. Choose the correct answer.

(a) 152 ÷ 4 =

(i) 38 (ii) 3.8 (iii) 380 (iv) 0.38

(b) 325 ÷ 8 =

(i) 40.625 (ii) 4.0625 (iii) 406.25 (iv) 40.6250

(c) 6.4 ÷ 8 =

(i) 0.08 (ii) 0.8 (iii) 8 (iv) 80

Section F: Division with Decimal Divisors

23. Convert the divisor into a whole number and solve.

(a) 12 ÷ 0.4

(b) 18 ÷ 0.6

(d) 4.5 ÷ 0.15

24. Find the quotients.

(a) 6.24 ÷ 1.2 =

(b) 9.36 ÷ 1.3 =

(d) 7.5 ÷ 0.25 =

25. Explain why both numbers must be multiplied by the same power of 10.

For example:

4.8 ÷ 0.6

Explain why we can change this into:

48 ÷ 6

26.

A car travels 180 km in 3.6 hours. Find its average speed in km per hour.

27.

A 7.5 kg bag of rice is divided equally into 6 packets. Find the weight of each packet.

Section G: Terminating and Repeating Decimals

28. Write the decimal form.

(a) 1/2 =

(b) 1/4 =

(d) 1/5 =

(e) 1/3 =

(f) 1/6 =

29.

Calculate 10 ÷ 3. Write the decimal answer and use dots to show that the decimal continues.

30.

Calculate 1 ÷ 7 to at least six decimal places. What repeating block do you observe?

31.

Write the first six decimal digits of 1 ÷ 7 and then write them again. What pattern do you notice?

32. True or False

(a) Every decimal division ends after a finite number of digits. True / False

(b) 1/3 has a repeating decimal expansion. True / False

(d) In a repeating decimal, a block of digits may repeat again and again. True / False

Section H: Decimal Word Problems

33.

A 4.8 m wooden stick is cut into 6 equal pieces. What is the length of each piece?

34.

A shopkeeper has 13.5 kg of flour. He distributes it equally among 15 families. How much flour does each family receive?

35.

Three litres of juice are shared equally among 8 children. How much juice does each child receive? Give the answer in litres and millilitres.

36.

A car uses 12.5 litres of petrol to travel 225 km. Find the distance travelled per litre.

37.

A rectangular garden is 12.5 m long and 8.4 m wide. Find its area.

Section I: Measurement and Conversion

38. Convert the following.

(a) 5.5 km = m

(b) 35 cm = m

(d) 68 g = kg

(e) 9.02 m = mm

(f) 125.5 ml = l

39.

A coin is 1.5 mm thick. What will be the height of a stack of 40 such coins? Give the answer in centimetres.

40.

A shelf is 150 cm long. Each book is 2.5 cm thick. How many complete books can be placed on the shelf if the books are placed side by side?

Section J: Leap Years and Decimal Thinking

41.

One solar year is approximately 365.2422 days. How many days are represented by 100 such solar years?

42.

Using 365.2422 days per year, find the approximate number of days in 400 years.

43.

A calendar year normally has 365 days. How many days are there in 100 ordinary calendar years if no leap days are added?

44.

If one extra day is added every fourth year, how many extra days are added in 100 years?

45. Think and explain.

Why is it useful to use decimal multiplication when comparing the calendar year with the actual time taken by Earth to orbit the Sun?

Section K: Mixed Challenge

46.

Given that 18 × 12 = 216, find:

(a) 1.8 × 1.2 =

(b) 18 × 1.2 =

(d) 180 × 0.12 =

47.

Given that 756 ÷ 36 = 21, find:

(a) 75.6 ÷ 3.6 =

(b) 7.56 ÷ 0.36 =

(d) 75.6 ÷ 360 =

48.

Find the missing divisor:

(a) 25 ÷ ______ = 0.25

(b) 25 ÷ ______ = 2.5

(d) 25 ÷ ______ = 0.025

49.

A rectangular playground is 24.5 m long and 15.2 m wide. Find its area.

50. Challenge Question

Using the digits 2, 4, 5, 8 and 0, make two decimal numbers using five digits in total. Try to make a product as close as possible to 100. Show your numbers and calculate the product.

Complete Answer Key

1. (a) tenth (b) hundredth (c) thousandth (d) tenths (e) hundredths (f) 5 (g) 25 (h) 0.7

2. (a) 4 + 0.2 + 0.06
(b) 8 + 0.3 + 0.005
(c) 12 + 0.04 + 0.007
(d) 0.6 + 0.008

3. (a) 0.7 (b) 0.43 (c) 0.215 (d) 0.09 (e) 0.006

4. (a) 7/10 (b) 34/100 (c) 125/1000 (d) 206/100

5. (a) 13.8 (b) 29 (c) 4.2 (d) 14.10 = 14.1 (e) 7.56

6. (a) 4.8 (b) 10.2 (c) 0.6 (d) 6.072

7. (a) 4.05 (b) 40.5 (c) 0.0405 (d) 405

8. (a) Greater than both numbers (b) Less than both numbers (c) Less than 5 but greater than 0.8 (d) Less than both numbers

9. (a) 2.5 (b) 0.78 (c) 0.8 (d) 0.08

10. ₹112.50

11. 12.5 × 4.5 = 56.25 km

12. 0.75 × 8 = 6 litres

13. 2.5 × 1.8 = 4.5 m²

14. 0.125 × 16 = 2 kg

15. (a) 4.75 (b) 0.475 (c) 0.0475 (d) 0.628 (e) 0.0628 (f) 0.00628

16.

Number	÷ 10	÷ 100	÷ 1000
18.6	1.86	0.186	0.0186
4.25	0.425	0.0425	0.00425
0.72	0.072	0.0072	0.00072
35.04	3.504	0.3504	0.03504

17. The decimal point moves to the left by as many places as there are zeroes in the divisor.

18. 5.6 ÷ 10 = 0.56 m

19. (a) 36 (b) 15.625 (c) 59.25 (d) 40.625

20. (a) 3.9 (b) 1.4 (c) 0.9 (d) 0.12 (e) 0.12

21. (a) 3.7 (b) 1.5625 (c) 1.2 (d) 0.15

22. (a) (i) 38 (b) (i) 40.625 (c) (ii) 0.8

23. (a) 30 (b) 30 (c) 9 (d) 30

24. (a) 5.2 (b) 7.2 (c) 36 (d) 30

25. Multiplying both dividend and divisor by the same number does not change the quotient. Therefore:
4.8 ÷ 0.6 = 48 ÷ 6 = 8.

26. 180 ÷ 3.6 = 50 km/h

27. 7.5 ÷ 6 = 1.25 kg

28. (a) 0.5 (b) 0.25 (c) 0.125 (d) 0.2 (e) 0.333… (f) 0.1666…

29. 10 ÷ 3 = 3.333…

30. 1 ÷ 7 = 0.142857142857…
The repeating block is 142857.

31. The first six digits are 142857. The same block repeats: 142857 142857…

32. (a) False (b) True (c) True (d) True

33. 4.8 ÷ 6 = 0.8 m

34. 13.5 ÷ 15 = 0.9 kg

35. 3 ÷ 8 = 0.375 litre = 375 ml

36. 225 ÷ 12.5 = 18 km per litre

37. 12.5 × 8.4 = 105 m²

38. (a) 5500 m (b) 0.35 m (c) 145 mm (d) 0.068 kg (e) 9020 mm (f) 0.1255 litre

39. 1.5 × 40 = 60 mm = 6 cm

40. 150 ÷ 2.5 = 60 books

41. 365.2422 × 100 = 36,524.22 days

42. 365.2422 × 400 = 146,096.88 days

43. 365 × 100 = 36,500 days

44. 100 ÷ 4 = 25 extra days

45. Decimal multiplication makes it easy to calculate the small difference between 365 days and the actual length of a solar year.

46. (a) 2.16 (b) 21.6 (c) 0.0216 (d) 21.6

47. (a) 21 (b) 21 (c) 2100 (d) 0.21

48. (a) 100 (b) 10 (c) 0.1 (d) 1000

49. 24.5 × 15.2 = 372.4 m²

50. One possible answer is:
4.5 × 22 = 99
The product is 99, which is 1 away from 100. Other valid arrangements may be possible depending on the digit-use rules followed.

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Class 7 Maths Chapter 4 Worksheet | Another Peek Beyond the Point