The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 2.7: EXPRESSING REPEATING DECIMALS

AS FRACTIONS OR MIXED NUMBERS

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Repeating decimals are represented by placing a bar over the digit or digits that repeat. All

repeating decimals can be represented as fractions. Follow the steps below:

1. Write an equation that statesn=the repeating decimal.


2. Multiply by a power of 10, depending on the number of digits that repeat. (If one digit
   repeats, multiply by 10; if two digits repeat, multiply by 100; if three digits repeat,
   multiply by 1,000; and so on.)


3. Subtract the original equation from the equation you wrote.


4. Solve the equation and simplify the answer.

EXAMPLE

Express 0. 75 as a fraction.

n= 0. 75

Because two digits repeat, multiply the equation by 100. 100 n= 75. 75

Subtract. 100 n= 75. 75

−n= 0. 75

99 n= 75

Solve the equation. n=

75

99

=

25

33

DIRECTIONS: Express each decimal as a fraction or mixed number.

1. 
   
   
   
   0. 1 2. 0. 23 3. 0. 72 4. 0. 5
   
   
   
   


2. 
   
   
   
   2. 81 6. 0. 03 7. 6. 512 8. 7. 162
   
   
   
   

CHALLENGE:Manny said that he found a shortcut to use when one digit

repeats: Just write the number over 9. He supported this statement with

the following examples: 0. 2 =

2

9

and 0. 4 =

4

9

.Roseannesaidthathis

shortcut is not valid because 0. 3 =

1

3

, which does not have a denominator

of 9. Who is correct?

61

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.