Recurring decimals to fractions
The Maths Habit
Is 0.999… equal to 1?
Yes
Work out
0.2222… × 10
2.2222…0.3838… × 100
38.3838…0.7777… × 10
7.7777…0.1212… × 100
12.1212…
- Recurring decimal
- A decimal with a digit, or a group of digits, that repeats forever.
0.6 = 0.666…0.15 = 0.151515…0.123 = 0.123123…
Write the first six decimal places
0.52
0.525252
x = 0.2424… Multiply by 10 or by 100?
100
x = 0.45
| x = | | 0 | . | 4 | 5 | 4 | 5 | 4 | 5 | … |
|---|
| 100x = | 4 | 5 | . | 4 | 5 | 4 | 5 | 4 | 5 | … |
|---|
× 100 moves every digit two places. The tails still match.
x = 0.45
Take x away from 100x. The tails cancel.
| 100x = | 4 | 5 | . | 4 | 5 | 4 | 5 | 4 | 5 | … |
|---|
| x = | | 0 | . | 4 | 5 | 4 | 5 | 4 | 5 | … |
|---|
| 99x = | 45 | | | | | | | | |
|---|
x = 0.45
99x = 45, so x = 4599 = 511
The quick way: x, 100x, take away, divide.
Write as a fraction
0.54
= 611
x = 0.5454…
100x = 54.5454…
99x = 54
Write as a fraction
0.63
= 711
Write as a fraction
0.54
= 611
Write as a fraction
0.12
= 433
Write as a fraction
0.54
= 611
Write as a fraction
0.4
= 49
Write as a fraction
0.54
= 611
Write as a fraction
0.07
= 799
Write as a fraction
0.54
= 611
Write as a fraction
0.81
= 911
Write as a fraction in its simplest form
0.83
Write 0.27 as a fraction in its simplest form.
518Write 1.2 as a mixed number.
129
x = 0.999… Use today's method to write x as a fraction.
9x = 9, so x = 1
Write 0.5 as a fraction.
59Write 0.36 as a fraction in its simplest form.
411Write 0.43 as a fraction in its simplest form.
1330Ravi says 0.12 = 12100. Is he right? Explain how you know.
No: 1299 = 433
Exit tickets to print
