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Roman Numerals

If u, v and w...

Question

If u, v and w are the digits of decimal system, then the rational number represented by 0.uwuvuvuvuv......is

(100 uw + 99 uv)/99

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(99uw + uv)/980

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(99uw + uv)/9900

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(9uw + 99uv)/900

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Solution

The correct option is C (99uw + uv)/9900
x =0.uwuvuvuvuv...
x = O.uwuv
(i) x 100
100x = uw. uv
(ii) x 100
10000x = uwuv - uv
(iii) - (ii)

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