X - Sequoyah Middle School

Cut along the dotted lines and glue into your notebook.

Changing Repeating Decimals to Fractions

Change 0.2 to a fraction in simplest form.

1

Question: How many digits are repeating? ________

Step 1: Let x represent the repeating decimal.

x = 0.22222

Hint: Write out several

extra repeating digits.

Step 2: Multiply both sides of the equation by 10, 100, 1000, etc.

(10 for 1 repeating digit, 100 for 2 repeating digits, etc. )

10 x = 2.22222

-

1 x = 0.22222

9 x= 2

Step 3: Bring down

original equation and

subtract both sides.

Hint: Line up decimal

points when subtracting.

Step 4: Solve equation for x.

9 x= 2

9

x=

9

2

9

Step 5: Simplify the

fraction, if necessary.

2

0.2 =_______

9

?2016 Math on the Move

Cut along the dotted lines and glue into your notebook.

Practice Problem #1

Change 0.36 to a fraction in simplest form.

2

Question: How many digits are repeating? ________

Step 1: Let x represent the repeating decimal.

x = 0.363636

Hint: Write out several

extra repeating digits.

Step 2: Multiply both sides of the equation by 10, 100, 1000, etc.

(10 for 1 repeating digit, 100 for 2 repeating digits, etc. )

100 x = 36.363636

-

1 x=

0.363636

99 x = 36

Step 3: Bring down

original equation and

subtract both sides.

Hint: Line up decimal

points when subtracting.

Step 4: Solve equation for x.

99 x = 36

99

x=

99

36

99

Step 5: Simplify the

fraction, if necessary.

4

0.36 =_______

11

?2016 Math on the Move

Cut along the dotted lines and glue into your notebook.

Practice Problem #2

Change 4.72 to a fraction in simplest form.

4.727272

100

472.7272

1

4.7272

99

99

468

99

4

72

8

= 4

99

11

Practice Problem #3

Change 0.83 to a fraction in simplest form.

0.83333

10

8.333333

1

0.83333

9

7.5

7.5

=

9

75

5

=

90

6

?2016 Math on the Move

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