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Grade 7: The Learning Equation Math
11.08 Terminating and Repeating Decimals 

Learning
Outcomes: The student will:
Review Methods for Converting
Fractions to Decimals 
Convert fraction to an equivalent fraction with a denominator that is a
power of ten before converting to a decimal. 
1/2 = 5/10 = 0.5
3/20 = 15/100 = 0.15
1/8 = 125/1000 = 0.125 
The decimal equivalent of a proper or improper fraction can be
calculated by dividing the numerator by the denominator. The result will be a terminating
or repeating decimal. 
3/4 = 0.75 
terminating decimal 
3/8 = 0.375 
terminating decimal 
4/15 = 0.0666... 
repeating decimal 
Method for Converting
Terminating Decimals to Fractions 
Use place value to convert the terminating decimal to a
fraction that is a power of ten. Reduce to lowest terms. The denominator of a
fraction converted from a terminating decimal will be a multiple of 2
and/or 5. 
0.5 = 5/10 = 1/2
0.2 = 2/10 = 1/5
0.15 = 15/100 = 3/20
0.125 = 125/1000 = 1/8 

Methods for Converting Singledigit
Decimal Numbers to Fractions 
To understand this lesson you need to understand what a singledigit
repeating decimal number is. 
Singledigit Repeating Decimal Numbers
 0.111...
 0.222...
 0.333...
 0.444...
 0.555...
 0.666...
 0.777...
 0.888...

Study the pattern when 9 is the denominator of a fraction.

 Complete the numerator divided by the denominator calculation with a calculator.
These are the quotients you should see when 9 is the denominator.

 1/9 = 1 9 = 0.111...
 2/9 = 2 9 = 0.222...
 3/9 = 3 9 = 0.333...
 4/9 = 4 9 = 0.444...
 5/9 = 5 9 = 0.555...
 6/9 = 6 9 = 0.666...
 7/9 = 7 9 = 0.777...
 8/9 = 8 9 = 0.888...

Any singledigit repeating decimal number can be
written as a fraction with 9 as the denominator and the repeating singledigit as the
numerator. 
 0.111... = 1/9
 0.222... = 2/9
 0.333... = 3/9
 0.444... = 4/9
 0.555... = 5/9
 0.666... = 6/9
 0.777... = 7/9
 0.888... = 8/9


Review:

Enrichment:
This lesson was limited to converting singledigit repeating decimal
numbers to fractions using patterns. If you wish to learn how to convert other
repeating decimals to fractions, try the convertor below:
Decimal to Fraction Convertor


Notes:
If you are trying to convert a repeating decimal
into a fraction, enter at least two (or more!) repetitions of the repeating part of
your decimal. For instance, if you are trying to convert:
0.676767...
into a fraction, enter at least 0.6767 (try 0.676767 also). 

place value, greatest common factor (GCF), mixed number, terminating
decimal, repeating decimal, simplest terms.

Prerequisite
Skills:
Decimal Conversions: Grade 7 Lesson
11.05
Ordering Numbers: Grade 7 Lesson 11.07
Fraction Conversions: Grade 7 Lesson
11.05

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