X - Sequoyah Middle School

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Changing Repeating Decimals to Fractions

Change 0.2 to a fraction in simplest form. Question: How many digits are repeating? ____1____

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

99

x= 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.

Question: How many digits are repeating? ____2____

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 99

x = 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

468

99

99

4

72 99

=

4

8 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 90

=

5 6

?2016 Math on the Move

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