Year 6 Maths: Writing Recurring Decimals as Percentages

Introduction

Hello, Year 6! Today, we are going to learn about how to write recurring decimals as percentages. A recurring decimal is a number that has a digit or a group of digits that repeat forever. For example, the decimal 0.333… goes on forever with the digit 3 repeating.

What is a Percentage?

Before we dive into recurring decimals, let’s quickly remember what a percentage is. A percentage is a way to express a number as a part of 100. So, when we say 50%, we mean 50 out of 100.

Understanding Recurring Decimals

Recurring decimals can be tricky, but they follow some simple patterns. Let’s look at a few examples:

• 0.333… is the same as 1/3.
• 0.666… is the same as 2/3.
• 0.142857… is the same as 1/7.

Converting Recurring Decimals to Percentages

To turn a recurring decimal into a percentage, follow these steps:

1. Identify the Decimal: Look at the number carefully. Is it a recurring decimal?
2. Convert to a Fraction: If you can, convert the recurring decimal into a fraction. For example, for 0.666…, we know it is 2/3.
3. Change the Fraction to a Percentage:
   • To do this, divide the numerator (top number) by the denominator (bottom number) and then multiply by 100.
   • For example, with 2/3: $$\frac{2}{3} \times 100 = 66.66… %$$
4. Round if Necessary: Sometimes, you may want to round the percentage to make it easier to read.

Example

Let’s convert 0.777… to a percentage:

1. Recognise that 0.777… is the same as 7/9.
2. Now convert the fraction: $$\frac{7}{9} \times 100$$ To calculate, do:
   • 7 divided by 9 = 0.777…
   • Then, multiply by 100 to get 77.77…

So, 0.777… is equal to 77.77%.

Key Rules

• Remember, recurring decimals have repeating digits.
• Convert to fractions when possible.
• Always multiply by 100 to convert a fraction to a percentage.

Tips and Tricks

• If you’re unsure about a recurring decimal, write it down and see if you can spot the repeating part.
• Use a calculator to help with fractions and percentages when you’re just starting.
• Practice with different recurring decimals to get familiar with the process!

Practice Questions

Easy Level (Questions 1-20)

1. Write 0.666… as a percentage.
2. Convert 0.888… to a percentage.
3. What is 0.333… as a percentage?
4. Change 0.111… to a percentage.
5. Convert 0.444… to a percentage.
6. Write 0.222… as a percentage.
7. What percentage is 0.555…?
8. Change 0.777… to a percentage.
9. Convert 0.999… to a percentage.
10. Write 0.121212… as a percentage.
11. What is 0.141414… as a percentage?
12. Convert 0.252525… to a percentage.
13. Write 0.363636… as a percentage.
14. Change 0.484848… to a percentage.
15. What is 0.676767… as a percentage?
16. Convert 0.787878… to a percentage.
17. Write 0.898989… as a percentage.
18. Change 0.101010… to a percentage.
19. What is 0.606060… as a percentage?
20. Convert 0.232323… to a percentage.

Medium Level (Questions 21-40)

21. Write 0.5555… as a percentage.
22. Convert 0.7878… to a percentage.
23. What percentage is 0.9999…?
24. Change 0.6666… to a percentage.
25. Convert 0.4444… to a percentage.
26. Write 0.3333… as a percentage.
27. What is 0.2222… as a percentage?
28. Change 0.141414… to a percentage.
29. Convert 0.272727… to a percentage.
30. Write 0.383838… as a percentage.
31. What percentage is 0.494949…?
32. Change 0.505050… to a percentage.
33. Convert 0.757575… to a percentage.
34. Write 0.8888… as a percentage.
35. What is 0.161616… as a percentage?
36. Change 0.191919… to a percentage.
37. Convert 0.161616… to a percentage.
38. Write 0.303030… as a percentage.
39. What is 0.959595… as a percentage?
40. Change 0.373737… to a percentage.

Hard Level (Questions 41-60)

41. Write 0.142857… as a percentage.
42. Convert 0.666666… to a percentage.
43. What percentage is 0.8333…?
44. Change 0.123123… to a percentage.
45. Convert 0.444444… to a percentage.
46. Write 0.333333… as a percentage.
47. What is 0.666666… as a percentage?
48. Change 0.111111… to a percentage.
49. Convert 0.101010… to a percentage.
50. Write 0.212121… as a percentage.
51. What percentage is 0.909090…?
52. Change 0.424242… to a percentage.
53. Convert 0.777777… to a percentage.
54. Write 0.585858… as a percentage.
55. What is 0.282828… as a percentage?
56. Change 0.474747… to a percentage.
57. Convert 0.494949… to a percentage.
58. Write 0.676767… as a percentage.
59. What is 0.888888… as a percentage?
60. Change 0.101010… to a percentage.

Answers and Explanations

Easy Level Answers

1. 66.66%
2. 88.88%
3. 33.33%
4. 11.11%
5. 44.44%
6. 22.22%
7. 55.55%
8. 77.77%
9. 99.99%
10. 12.12%
11. 14.14%
12. 25.25%
13. 36.36%
14. 48.48%
15. 67.67%
16. 78.78%
17. 89.89%
18. 10.10%
19. 60.60%
20. 23.23%

Medium Level Answers

21. 55.55%
22. 78.78%
23. 99.99%
24. 66.66%
25. 44.44%
26. 33.33%
27. 22.22%
28. 14.14%
29. 27.27%
30. 38.38%
31. 49.49%
32. 50.50%
33. 75.75%
34. 88.88%
35. 16.16%
36. 19.19%
37. 16.16%
38. 30.30%
39. 95.95%
40. 37.37%

Hard Level Answers

41. 14.29%
42. 66.67%
43. 83.33%
44. 12.31%
45. 44.44%
46. 33.33%
47. 66.67%
48. 11.11%
49. 10.10%
50. 21.21%
51. 90.91%
52. 42.42%
53. 77.78%
54. 58.59%
55. 28.28%
56. 47.47%
57. 49.49%
58. 67.67%
59. 88.89%
60. 10.10%

I hope you enjoyed learning about writing recurring decimals as percentages! Remember to practice, and soon it will feel easy! Happy Maths!