1970 AHSME Problems/Problem 10
Problem
Let be an infinite repeating decimal with the digits and repeating. When is written as a fraction in lowest terms, the denominator exceeds the numerator by
Solution
Multiplying by gives . Subtracting the first equation from the second gives , and all the other repeating parts cancel out. This gives . Subtracting the numerator from the denominator gives .
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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