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Why is the finite cyclic decimal reduced to a fraction with a denominator of 9? See page p 13 of Shanghai Science and Technology Edition for details.
Cyclic decimal can be written as x10n-x10 (n-1) = x.

X 10 n-x = a (x is the original number, n is the cyclic number, and a is the cyclic number).

x=a/( 10^n- 1)

The first number of 10 n- 1 is naturally 9.

However, if this denominator can be simplified, the first number of the simplified denominator is not necessarily 9.

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