Converting Repeating Decimals to Fractions

NOTES: Converting a Repeating Decimal into a Fraction

Look at some patterns of repeating decimals:

1. 0.1= 1

9

2.

0.2=

2 9

3.

0.3=

=

simplified:

10.

0.09=

9 99

= simplified:

1 11

11.

0.18=

18 99

= simplified:

2 11

4. 0.4=

5.

0.5=

5 9

6.

0. =

6 9

=

simplified:

7. 0.7= 7

9

8.

0.8=

9. 0.9= 9 = 1

9

What pattern do you see when 1 digit

12.

0.27=

99

= simplified:

3 11

13.

0.18= 18 = simplified: 2

99

11

14.

0.13=

99

15.

0.37=

99

16.

0.56=

repeats?_________________________________________ ___________________________________________________

17.

0.123= 123

999

18.

0.421=

999

19.

0.563=

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 # =# 0.

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.

So,

0.23=

21 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=

#5:

0.4276=

#7:

0.018=

#4:

0.427=

#6:

0.235=

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