x is an integer such that ‎1≤x≤9, Prove that 0.(0x)recurring=x/99

r=0.0.x.

r=0.0x0x0x0x....

100r=x.0x0x0x     (1)

10,000r=x0x.0x0x0x      (2)

(2) - (1):  9,900r=x00

r=x00/9,990        r=x/99

Answered by Ellie E. Maths tutor

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