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Write the rational number $0.772772772\ldots$ as a fraction.

Write the rational number $0.69696969\ldots$ as a fraction.

Solution

The three-digit number $772$ repeats after the decimal. So we will make use of the three-digit denominator $999\text{.}$ And we have $\frac{772}{999}\text{.}$

The two-digit number $69$ repeats after the decimal. So we will make use of the two-digit denominator $99\text{.}$ And we have $\frac{69}{99}\text{.}$ But this fraction can be reduced to $\frac{23}{33}\text{.}$

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