SOLUTION: How do you change .78 repeating and .66 repeating into a fraction?

Question 7020: How do you change .78 repeating and .66 repeating into a fraction?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Change 0.7878... to a fraction.
Let n = 0.7878... Multiply both sides by 100 (by 100 when there are two repeating decimal digits)
100n = 78.7878... Subtract n from 100n.
99n = 78 Divide both sides by 99
n = 78/99 but n is 0.7878..., so
0.7878... = 78/99
Similarly with 0.66...
Let n = 0.66... Multiply both sides by 10 (by 10 when there is only one repeating digit)
10n = 6.66... Subtract n from 10n.
9n = 6 Divide both sides by 9.
n = 6/9 but n is 0.66..., so
0.66... = 6/9
Check using your calculator. 78/99 = 0.787878... and 6/9 = 0.6666...
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