**Activity:
Repeating and Terminating Decimals**

Every fraction (i.e. rational number) can be written in decimal form.

So how do you rename fractions (the terminating kind) as decimals?

First, find an equivalent fraction that has 10, 100, 1000, etc. in its
denominator. For example.

1/2 = 5/10

3/4 = 75/100

5/8 = 625/1000

** Quick Review **“Cloning” fractions

Two fractions are clones if they are equivalent.

1/2 is the clone of 5/10. Why? If you multiply numerator and denominator by the same number you have a cloned or equivalent fraction.

Another way to write fractions that have 10, 100, 1000, etc in the denominator is to write it in decimal notation.

75/100 is read “seventy five hundredths” and equals .75

BTW - If you say .75 with meaning you say “75 hundredths”, not “point 75”

Some fractions are not as nice. They have numbers that repeat in their decimal expression. For example,

1/3 can’t be cloned to have 10, 100. 1000, etc. in its denominator. Why? Because you can’t come up with a whole number to clone with for 3 since 3 does not divide into 10, 100, 1000, etc. evenly.

So the best we can do is to treat 1/3 as a division problem (which it is) and do the division.

__ 0.3333333
__3 | 1.0000000

1/3 = 0.3333333......

Here 3 is the repeating number.

Some fractions repeat more than 1 number. For example, try

1/11

You should see that 0 and 9 repeat.

Create the
spreadsheet below:

Click on Spreadsheet above to download it.

Resources

Lesson on Repeating and Terminating Decimals by Dana T. Johnson

Repeating Decimal Calculator

Handy
Java tool for determining whether a fraction terminates or not.

For more on this tool see repeating
or terminating? by Jeff LeMieux