math

ACTIVITY 12: TERMINATE
OR REPEAT?
Every fraction has a decimal equivalent that either terminates (for example, ) or
repeats (for example, ). Work with a group to discover which fractions have terminating
decimals and which have repeating decimals. You may assume that the numerator
of each fraction you consider is and focus your attention on the denominator. As you complete
the table below, you will find that the key to this question lies with the prime factorization
of the denominator.
2
9
� 0.2
1
4
� 0.25
Prime Factorization
Fraction Decimal Form Terminate? of the Denominator
1
12
1
11
1
10
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
State a general rule describing which fractions have decimal forms that terminate and
which have decimal forms that repeat.
Now test your rule on at least three new fractions. That is, be able to predict whether a
fraction such as or has a terminating decimal or a repeating decimal. Then confirm
your prediction.
1
30
1
25
360

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