Converting Decimal Representations of Rational Numbers to Fraction Representations

Converting Decimal Representations of Rational Numbers to Fraction Representations

1. The solution for all the parts of this take advantage of the repeating structure of the decimal expansions. Namely, by multiplying by a suitable power of 10 (namely, 10r where r is the length of the repeating segment in the decimal expansion) and subtracting the original number, we can get a multiple of x with a finite decimal expansion.