Step 2: Converting Repeating Decimals to Fractions
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
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