Year 6 Maths: Recurring Decimals

What Are Recurring Decimals?

Hello, Year 6! Today, we’re going to learn about something called recurring decimals. Recurring decimals are special numbers that have a repeating pattern in their decimal part.

What Does This Mean?

When you divide two numbers, you might get a decimal that goes on forever. For example:

• If you divide 1 by 3, you get 0.3333… This means the 3 keeps repeating.

We can write this in a simpler way using a special symbol called a bar. So, we write:

$$\frac{1}{3} = 0.\overline{3}$$

This shows that the 3 keeps going forever.

More Examples

Let’s look at some more examples of recurring decimals:

• 1 divided by 6 gives us 0.1666… We write this as:$$\frac{1}{6} = 0.1\overline{6}$$
• 2 divided by 11 gives us 0.181818… We write this as:$$\frac{2}{11} = 0.\overline{18}$$

Key Rules

1. Recognising Recurring Decimals: Look for numbers that repeat in the decimal places.
2. Writing Recurring Decimals: Use a bar over the repeating part of the decimal to show it goes on forever.
3. Converting: You can convert a recurring decimal back into a fraction.

Tips and Tricks

• Practice: The more you practice, the easier it gets!
• Use a calculator: When dividing, see if the decimal keeps going or starts to repeat.
• Draw it: Sometimes drawing a number line can help you see where the decimal is going.

Questions

Easy Level Questions

1. What is 1 divided by 3 as a decimal?
2. Write 0.6666… using a bar.
3. What is 2 divided by 3 in decimal form?
4. Write 0.8888… using a bar.
5. What is 1 divided by 9 as a decimal?
6. Write 0.101010… using a bar.
7. Is 0.25 a recurring decimal? (Yes or No)
8. Write 0.4444… using a bar.
9. What is 5 divided by 6 as a decimal?
10. Write 0.7777… using a bar.
11. What is 1 divided by 7 as a decimal?
12. Write 0.121212… using a bar.
13. Is 0.5 a recurring decimal? (Yes or No)
14. What is 3 divided by 4 as a decimal?
15. Write 0.232323… using a bar.
16. What is 4 divided by 11 as a decimal?
17. Write 0.6666… using a bar.
18. What is 2 divided by 7 as a decimal?
19. Write 0.5555… using a bar.
20. What is 1 divided by 12 as a decimal?

Medium Level Questions

1. Convert 0.3333… to a fraction.
2. How can you express 0.6666… as a fraction?
3. What is the decimal for 1 divided by 6?
4. Write 0.181818… as a fraction.
5. Find the decimal for 5 divided by 9.
6. Express 0.292929… as a fraction.
7. What is 7 divided by 9 as a decimal?
8. Convert 0.4444… to a fraction.
9. What is 2 divided by 11 as a decimal?
10. Write 0.787878… as a fraction.
11. What is 3 divided by 7 as a decimal?
12. Convert 0.99… to a fraction.
13. What is 8 divided by 11 as a decimal?
14. Write 0.161616… as a fraction.
15. What is the fraction for 0.8888…?
16. Convert 0.272727… to a fraction.
17. What is the decimal for 1 divided by 8?
18. Write 0.353535… as a fraction.
19. What is 9 divided by 11 as a decimal?
20. Convert 0.121212… to a fraction.

Hard Level Questions

1. If 0.ABABAB… = x, what is the value of x in fraction form?
2. Express 0.123123… as a fraction.
3. Convert 2.6666… to a mixed number.
4. If x = 0.454545…, find the value of x in fraction form.
5. Write the decimal for 5 divided by 12.
6. If 0.ABAB… = x, how do you express it in terms of x?
7. Convert 0.217171… to a fraction.
8. What is the decimal for 7 divided by 12?
9. Write 0.828282… as a fraction.
10. If 0.3333… = x, what is the value of x?
11. Convert 0.989898… to a fraction.
12. What is 11 divided by 27 as a decimal?
13. Write 0.414141… as a fraction.
14. If x = 0.6666…, what is the value of 3x?
15. Find the decimal for 13 divided by 33.
16. Express 0.636363… as a fraction.
17. What is the fraction for 0.101010…?
18. Convert 0.3333… + 0.6666… to a fraction.
19. What is 1 divided by 22 as a decimal?
20. Write the decimal for 8 divided by 15.

Answers

Easy Level Answers

1. 0.3333…
2. 0.\overline{6}
3. 0.6666…
4. 0.\overline{8}
5. 0.1111…
6. 0.\overline{10}
7. No
8. 0.\overline{4}
9. 0.8333…
10. 0.\overline{7}
11. 0.142857…
12. 0.\overline{12}
13. No
14. 0.75
15. 0.\overline{23}
16. 0.363636…
17. Yes
18. 0.\overline{5}
19. 0.8333…
20. 0.0833…

Medium Level Answers

1. $$\frac{1}{3}$$
2. $$\frac{2}{3}$$
3. 0.1666…
4. $$\frac{2}{11}$$
5. 0.5555…
6. $$\frac{29}{99}$$
7. 0.7777…
8. $$\frac{4}{9}$$
9. 0.181818…
10. $$\frac{78}{99}$$
11. 0.428571…
12. 1
13. 0.727272…
14. $$\frac{8}{9}$$
15. $$\frac{27}{99}$$
16. $$\frac{9}{33}$$
17. 0.125
18. $$\frac{1}{3}$$
19. 0.818181…
20. $$\frac{1}{8}$$

Hard Level Answers

1. $$\frac{AB}{99}$$
2. $$\frac{123}{990}$$
3. $$2 \frac{2}{3}$$
4. $$\frac{5}{11}$$
5. 0.41666…
6. $$\frac{1}{10}$$
7. $$\frac{217}{990}$$
8. 0.5833…
9. $$\frac{82}{99}$$
10. $$\frac{1}{3}$$
11. $$\frac{99}{100}$$
12. 0.4074…
13. $$\frac{41}{99}$$
14. 2
15. 0.3939…
16. $$\frac{63}{99}$$
17. $$\frac{1}{9}$$
18. 1
19. 0.04545…
20. 0.53333…

I hope this helps you understand recurring decimals better! Keep practicing, and you’ll get the hang of it in no time!