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Decimal to Fraction

Step 2: Converting repeating decimals to fractions

Picture of Converting repeating decimals to fractions
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Converting repeating decimals to fractions it a little bit harder than typing it in on a calculator because the calculator doesn't have an infinitely long screen. Still it can be done with relative ease if you just think it simple. Converting repeating decimals requires a little algebraic manipulation.

1. Let x equal your repeating decimal. Call this equation 1 eg, x=0.6666666...

2. Multiply both sides of your previous expressions by 10 . Call this equation 2 eg, 10x=6.6666666...

3.Subtract equation 2 from equation 1. eg, 9x=6 (see picture for clearer explanation)

4.Solve for x. eg, x=6/9
=2/3

5. But x is also equal to 0.66666..., therefore 0.666... is equal to 2/3.

NOTE: In harder repeating decimals such as decimals which repeat a string of number may need you to multiply by 100 or 1000 etc to allow the repeats behind the decimal point to cancel in the subraction
 
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