BellaRose8133 BellaRose8133
  • 08-08-2018
  • Mathematics
contestada

Xpress 8.54545454545... as a rational number, in the form pq where p and q are positive integers with no common factors.

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zexius
zexius zexius
  • 08-08-2018

If you mean p/q, then this is how you do it:

[tex] \textrm{Let x represent the recurring decimal.}

x = 8.54545...

100x = 854.54545...

\textrm{Subtract first expression from second expression.}

100x - x = 99x

854.54545... - 8.54545... = 846

\therefore 99x = 846

\textrm{Isolate x term by dividing by 99 on both sides of the expression.}

x = 846\div99 [/tex]

[tex] x = \frac{846}{99} = \frac{94}{11} [/tex]

Therefore your final answer is 94/11, where p is 94 and q is 11.

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