Teaching Notes 2.6: Expressing Terminating Decimals
as Fractions or Mixed Numbers
Expressing terminating decimals as fractions is a relatively straightforward procedure. Two
common errors include using an incorrect decimal place in writing the fraction and failing to use
the negative sign with negative numbers.- Explain that a terminating decimal is a decimal that does not repeat. For example, 0.5, 0.894,
and−2.35 are terminating decimals. - Explain that terminating decimals can be expressed as fractions or mixed numbers. (You
might mention that repeating decimals can also be expressed as fractions or mixed numbers.) - Review the place value chart and examples on the worksheet with your students. Explain
that they must consider the number of decimal places to the right of the decimal point when
they write a decimal as a fraction. Make sure that your students fully understand place value.
A decimal that ends in the tenths place will equal a fraction with a denominator of 10; a dec-
imal that ends in the hundredths place will equal a fraction with a denominator of 100; a
decimal that ends in the thousandths place will equal a fraction with a denominator of 1,000;
and so on. - Remind your students that a negative decimal must be expressed as a negative fraction and
that fractions should always be simplified.
EXTRA HELP:
You can always double-check your answer by changing the fraction or mixed number to a decimal.ANSWER KEY:
(1)39
50
(2)−
3
10
(3)− 1
7
100
(4) 15
33
40
(5)− 6
4
25
(6)−
1
40
(7) 18
3
4
(8)− 20
1
100
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(Challenge)There are two errors.− 315
100
= 3
5
20
. The fraction is simplified incorrectly and the
negative sign is missing. The correct answer is− 315
100
=− 3
3
20
.
.
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58 THE ALGEBRA TEACHER’S GUIDE