Posted by **gertrude** on Wednesday, October 8, 2008 at 2:52pm.

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