Converting Repeating Decimals to Fractions

NOTES: Converting a Repeating Decimal into a Fraction

Look at some patterns of repeating decimals:

1

1. 0.1?=

9

2

2. 0.2?=

9

?

3. 0.3?= = simplified:

?

?

?

?

4. 0.4?=

?

10.

????= 9 = simplified: 1

0.09

11.

????= 18 = simplified: 2

0.18

12.

????=

0.27

13.

????= 18 = simplified: 2

0.18

14.

????=

0.13

15.

????=

0.37

16.

????=

0.56

17.

?????= 123

0.123

18.

?????=

0.421

19.

?????=

0.563

99

99

? = 6 = simplified:

6. 0.?

9

?

99

?

?

3

11

11

??

99

9

8. 0.8?=

= simplified:

99

?

7

7. 0.7?=

11

??

5

5. 0.5?=

9

11

??

99

9

9. 0.9?= = 1

9

What pattern do you see when 1 digit

repeats?_________________________________________

??

??

999

___________________________________________________

???

999

???

???

What pattern do you see when 2 or more

digits repeat?________________________________

___________________________________________________

We can quickly determine:

The numerator is the same as the number under the ??????????????????

??? ???????? (repeating numbers).

The denominator is 9 for one place under the ??????????????????

??? ????????, 99 for two places under the

bar notation and 999 for 3 places under the bar notation and so on.

What if the decimal is of a form where not all the numbers repeat? Always simplify answer.

Take Notes- Video:

?????????=?????????? ??????? ??? ?????? ???? ???? ??? ?????? ??? ??? ?????? ??????.

???????????=?????? ?? ?????? ???? ??????=# ?? 9¡ä ? ??? ??? # ?? ?????? ???? ?? ??? ??????=# ?? 0¡ä ?.

Example #1: 0.23?=

??

??

Numerator:

What number is not repeating? 2

What is the entire number? 23

What is the difference between both numbers? 21 (this is the numerator)

Denominator:

How many digits repeat?

Only 1 digit repeats so the denominator will have a 9

How many digits do not repeat? Only 1 digit doesn¡¯t repeat, so the denominator will have a 0.

21

So, 0.23?=

90

????

Example #2: 0.325

Numerator:

What number is not repeating? _____

What is the entire number?

_____

What is the difference between both numbers? ______ (this is the numerator)

Denominator:

How many digits repeat? _______

(this is the number of 9¡¯s in the denominator)

How many digits do not repeat? _______

(this is the number of 0¡¯s in the denominator)

???

???? =

So, 0.325

???

#3: 0.35?=

??

??

????=

#4: 0.427

???

???

?????=

#5: 0.4276

#6: 0.235?=

????

????

???

???

????=

#7: 0.018

??

???

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