Quote:
Originally Posted by MAS1
Here are a couple of examples for terminating decimals:
1. 0.465
Look at a nonzero 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 nonterminating, 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!

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