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Old 11-30-2010   #9
Lisasmith111
 
Join Date: Nov 2010
Posts: 36
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Quote:
Originally Posted by MAS1 View Post
Here are a couple of examples for terminating decimals:

1. 0.465
Look at a non-zero digit which is in the smallest place. In this case it is the 5 in the thousandths place. This means the denominator for your fraction will be 1000. Now write the digits "465" in the numerator. You should have:
465/1000 which is four hundred sixty five thousandths.
Now see if you can simplify the fraction. 5 is a factor of both the numerator and denominator so divide both by 5 giving
93/200

2. 2.76
Ignore the whole number part for now.
0.76 = 76/100 = 38/50 = 19/25
Now add the whole number part back in creating the mixed number 2 19/25

To find the fraction for non-terminating, repeating decimals:

1. 0.33333...
Let x = 3.33333...
then 10x = 3.33333...
10x - x = 3.3333... - 0.3333...
9x = 3 (All of the 3's to the right of the decimal place cancel out)
x = 3/9 = 1/3

2. 0.166666...
Let x = 0.166666...
10x = 1.66666...
10x - x = 1.66666... - 0.1666666...
9x = 1.5
18x = 3
x = 3/18 = 1/6

3. 0.142857142857142857...
x = 0.142857142857142857...
1000000x = 142857.142857142857142857...
1000000x - x = 142857
999999x = 142857
x = 142857/999999 = 15873/111111 = 5291/37037 = 1/7

Hope this helps!
That is a very useful post - I looked at a book on Engineering maths and did not understand how to do terminating decimals as fractions. However, your approach is nice, simple and direct. Thanks

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