Year 4 Maths: Writing Decimals as Fractions

Introduction to Decimals and Fractions

Hello, Year 4! Today, we’re going to learn about how to write decimals as fractions. Don’t worry; it’s not as tricky as it sounds! Decimals and fractions are two ways of showing the same value.

What is a Decimal?

A decimal is a number that has a point called a decimal point. For example, in the number 0.5, “0” is on the left side of the decimal point, and “5” is on the right side.

What is a Fraction?

A fraction shows a part of a whole. It has two numbers: the top number (called the numerator) and the bottom number (called the denominator). For example, in the fraction

How to Write Decimals as Fractions

Step 1: Understand the Place Value

The first step is to understand where the decimal is. The number to the right of the decimal point tells us the place value.

• The first place is tenths (0.1).
• The second place is hundredths (0.01).

For example:

• 0.3 means 3 tenths: $$\frac{3}{10}$$ .
• 0.25 means 25 hundredths: $$\frac{25}{100}$$ .

Step 2: Write the Fraction

Now, we can write the decimal as a fraction:

1. Count how many places are to the right of the decimal point.
2. Write the number without the decimal as the numerator.
3. Use 10 for one decimal place, 100 for two decimal places, and so on, as the denominator.

Step 3: Simplify the Fraction (if needed)

Sometimes, we can make the fraction simpler. For example:

• $$\frac{25}{100}$$ can be simplified to $$\frac{1}{4}$$ because both 25 and 100 can be divided by 25.

Key Rules to Remember

1. Count the places: How many digits are after the decimal?
2. Use the right denominator: 10 for tenths, 100 for hundredths, etc.
3. Simplify when you can: Make the fraction smaller if possible.

Tips and Tricks

• Write down the decimal and the fraction next to each other to help you see the difference.
• Practice with different examples to get better.
• Remember that every fraction can be written as a decimal and every decimal can be written as a fraction!

Questions

Easy Level Questions (1-20)

1. Write 0.5 as a fraction.
2. Write 0.9 as a fraction.
3. Write 0.2 as a fraction.
4. Write 0.75 as a fraction.
5. Write 0.1 as a fraction.
6. Write 0.6 as a fraction.
7. Write 0.25 as a fraction.
8. Write 0.4 as a fraction.
9. Write 0.8 as a fraction.
10. Write 0.05 as a fraction.
11. Write 0.3 as a fraction.
12. Write 0.15 as a fraction.
13. Write 0.7 as a fraction.
14. Write 0.95 as a fraction.
15. Write 0.12 as a fraction.
16. Write 0.85 as a fraction.
17. Write 0.45 as a fraction.
18. Write 0.33 as a fraction.
19. Write 0.60 as a fraction.
20. Write 0.99 as a fraction.

Medium Level Questions (21-40)

21. Write 0.36 as a fraction.
22. Write 0.2 as a fraction and simplify it.
23. Write 0.55 as a fraction.
24. Write 0.18 as a fraction and simplify it.
25. Write 0.44 as a fraction.
26. Write 0.68 as a fraction.
27. Write 0.11 as a fraction.
28. Write 0.27 as a fraction.
29. Write 0.90 as a fraction and simplify it.
30. Write 0.72 as a fraction.
31. Write 0.8 as a fraction and simplify it.
32. Write 0.62 as a fraction.
33. Write 0.39 as a fraction and simplify it.
34. Write 0.4 as a fraction and simplify it.
35. Write 0.08 as a fraction.
36. Write 0.22 as a fraction and simplify it.
37. Write 0.57 as a fraction.
38. Write 0.13 as a fraction.
39. Write 0.78 as a fraction and simplify it.
40. Write 0.02 as a fraction.

Hard Level Questions (41-60)

41. Write 0.125 as a fraction and simplify it.
42. Write 0.375 as a fraction.
43. Write 0.666 as a fraction.
44. Write 0.45 as a fraction and simplify it completely.
45. Write 0.85 as a fraction and simplify it fully.
46. Write 0.99 as a fraction and simplify it.
47. Write 0.007 as a fraction.
48. Write 0.555 as a fraction and simplify it.
49. Write 0.333 as a fraction.
50. Write 0.123 as a fraction.
51. Write 0.875 as a fraction.
52. Write 0.040 as a fraction and simplify it.
53. Write 0.500 as a fraction.
54. Write 0.250 as a fraction and simplify it.
55. Write 0.888 as a fraction.
56. Write 0.062 as a fraction and simplify it.
57. Write 0.3333 as a fraction.
58. Write 0.142857 as a fraction.
59. Write 0.66667 as a fraction and simplify it.
60. Write 0.025 as a fraction.

Answers

Easy Level Answers

1. $$\frac{5}{10}$$ (simplifies to $$\frac{1}{2}$$ )
2. $$\frac{9}{10}$$
3. $$\frac{2}{10}$$ (simplifies to $$\frac{1}{5}$$ )
4. $$\frac{75}{100}$$ (simplifies to $$\frac{3}{4}$$ )
5. $$\frac{1}{10}$$
6. $$\frac{6}{10}$$ (simplifies to $$\frac{3}{5}$$ )
7. $$\frac{25}{100}$$ (simplifies to $$\frac{1}{4}$$ )
8. $$\frac{4}{10}$$ (simplifies to $$\frac{2}{5}$$ )
9. $$\frac{8}{10}$$ (simplifies to $$\frac{4}{5}$$ )
10. $$\frac{5}{100}$$ (simplifies to $$\frac{1}{20}$$ )
11. $$\frac{3}{10}$$
12. $$\frac{15}{100}$$ (simplifies to $$\frac{3}{20}$$ )
13. $$\frac{7}{10}$$
14. $$\frac{95}{100}$$ (simplifies to $$\frac{19}{20}$$ )
15. $$\frac{12}{100}$$ (simplifies to $$\frac{3}{25}$$ )
16. $$\frac{85}{100}$$ (simplifies to $$\frac{17}{20}$$ )
17. $$\frac{45}{100}$$ (simplifies to $$\frac{9}{20}$$ )
18. $$\frac{33}{100}$$
19. $$\frac{60}{100}$$ (simplifies to $$\frac{3}{5}$$ )
20. $$\frac{99}{100}$$

Medium Level Answers

21. $$\frac{36}{100}$$ (simplifies to $$\frac{9}{25}$$ )
22. $$\frac{2}{10}$$ (simplifies to $$\frac{1}{5}$$ )
23. $$\frac{55}{100}$$ (simplifies to $$\frac{11}{20}$$ )
24. $$\frac{18}{100}$$ (simplifies to $$\frac{9}{50}$$ )
25. $$\frac{44}{100}$$ (simplifies to $$\frac{11}{25}$$ )
26. $$\frac{68}{100}$$ (simplifies to $$\frac{17}{25}$$ )
27. $$\frac{11}{100}$$
28. $$\frac{27}{100}$$
29. $$\frac{90}{100}$$ (simplifies to $$\frac{9}{10}$$ )
30. $$\frac{72}{100}$$ (simplifies to $$\frac{18}{25}$$ )
31. $$\frac{8}{10}$$ (simplifies to $$\frac{4}{5}$$ )
32. $$\frac{62}{100}$$ (simplifies to $$\frac{31}{50}$$ )
33. $$\frac{39}{100}$$
34. $$\frac{4}{10}$$ (simplifies to $$\frac{2}{5}$$ )
35. $$\frac{8}{100}$$ (simplifies to $$\frac{2}{25}$$ )
36. $$\frac{22}{100}$$ (simplifies to $$\frac{11}{50}$$ )
37. $$\frac{57}{100}$$
38. $$\frac{13}{100}$$
39. $$\frac{78}{100}$$ (simplifies to $$\frac{39}{50}$$ )
40. $$\frac{2}{100}$$ (simplifies to $$\frac{1}{50}$$ )

Hard Level Answers

41. $$\frac{125}{1000}$$ (simplifies to $$\frac{1}{8}$$ )
42. $$\frac{375}{1000}$$ (simplifies to $$\frac{3}{8}$$ )
43. $$\frac{666}{1000}$$ (simplifies to $$\frac{2}{3}$$ )
44. $$\frac{45}{100}$$ (simplifies to $$\frac{9}{20}$$ )
45. $$\frac{85}{100}$$ (simplifies to $$\frac{17}{20}$$ )
46. $$\frac{99}{100}$$
47. $$\frac{7}{1000}$$
48. $$\frac{555}{1000}$$ (simplifies to $$\frac{111}{200}$$ )
49. $$\frac{333}{1000}$$
50. $$\frac{123}{1000}$$
51. $$\frac{875}{1000}$$ (simplifies to $$\frac{7}{8}$$ )
52. $$\frac{40}{1000}$$ (simplifies to $$\frac{1}{25}$$ )
53. $$\frac{500}{1000}$$ (simplifies to $$\frac{1}{2}$$ )
54. $$\frac{250}{1000}$$ (simplifies to $$\frac{1}{4}$$ )
55. $$\frac{888}{1000}$$ (simplifies to $$\frac{222}{250}$$ )
56. $$\frac{62}{1000}$$ (simplifies to $$\frac{31}{500}$$ )
57. $$\frac{3333}{10000}$$
58. $$\frac{142857}{1000000}$$ (this is a repeating decimal!)
59. $$\frac{66667}{100000}$$
60. $$\frac{25}{1000}$$ (simplifies to $$\frac{1}{40}$$ )

Great job today, Year 4! Keep practicing writing decimals as fractions, and soon it will feel easy! If you have any questions, feel free to ask!