Terminating and Repeating Decimals

Grade 7: The Learning Equation Math

11.08 Terminating and Repeating Decimals

Refresher pp 16-17

The student will:

convert from terminating decimals to fractions.

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

convert from single-digit repeating decimal numbers to fractions, using patterns.

Methods for Converting Single-digit Decimal Numbers to Fractions

To understand this lesson you need to understand what a single-digit repeating decimal number is.

Single-digit 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 single-digit repeating decimal number can be written as a fraction with 9 as the denominator and the repeating single-digit 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 single-digit 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).

Converting Repeating Decimals to Fractions

Key Terms:

A-E

F-J

K-O

P-R

S-Z

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