828/MR00. problem / Math - Solved Math Problems

MR-828 / 828. problem

Prove that 0.117117117... is a rational number.

$x = 0, 117117117 . . .$

$1000 \cdot x = 117, 117117117 . . .$

$1000 \cdot x - x = 117, 117117117 . . . - 0, 117117117 . .$

$999 \cdot x = 117$

$x = \frac{117}{999}$

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