Page 866 - Algebra 1

Repeating Decimals and Equivalent Fractions
Skills Bank Lesson 6
A terminating decimal, such as 0.75, has a finite number of decimal places.
A repeating decimal, such as 0.333... and 0.353535..., has one or more digits after the
decimal point repeating indefinitely. A repeating decimal can be written with three dots
or a bar over the digit or digits that repeat, such as 0.3 and 0.35.
Writing an Equivalent Fraction for a Terminating Decimal
Write each decimal as a fraction in simplest form.
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Example
1
a. 0.35 SOLUTION
_ 0.35= 35
Thedecimalisinthehundredthsplace,souse100asthedenominator. Simplify.
The decimal is in the tenths place, so use 10 as the denominator.
Writing an Equivalent Fraction for a Repeating Decimal
100 __
35 = 7 100 20
b. 1.9 SOLUTION
1.9 = 1_9 10
Example
2
Write 0.272727... as a fraction.
SOLUTION
To eliminate the repeating decimal, subtract the same repeating decimal.
n= 100n =
11
Skills Bank Practice
Write an equivalent fraction in simplest form for each decimal. a. 0.85 b. 1.75 c. 0.575757... e. 0.48 f. 1.25 g. 0.363636...
100n= -n=
0.272727... 27.272727...
27.272727...
-0.272727... ______
Let n represent the fraction equivalent to 0.272727...
Since 2 digits repeat, multiply both sides of the equation by
102 or 100.
Subtract the original equation. Combine like terms.
Divide both sides by 99 and simplify.
__ 99n =
27 __
27 = 3 99 11
n=
0.272727... is equivalent to _3 .
d. 0.81 h. 0.44−4
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Skills Bank 851
SKILLS BANK