razerocfu3107 razerocfu3107
  • 03-07-2019
  • Mathematics
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Show that the following number is rational: 7.526262626... show all work, discrete math

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konrad509
konrad509 konrad509
  • 03-07-2019

[tex]x=7.5\overline{26}\\10x=75.\overline{26}\\1000x=7526.\overline{26}\\1000x-10x=7526.\overline{26}-75.\overline{26}\\990x=7451\\x=\dfrac{7451}{990}[/tex]

It can be expressed as a fraction with integer numerator and denominator, so it's a rational number.

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