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KonstantinChe [14]
2 years ago
7

Is 2.73234(34 repeating) rational or irrational?

Mathematics
1 answer:
Fittoniya [83]2 years ago
5 0

It's rational because of the repeating digits.

We have

<em>x</em> = 2.732<u>343434</u>…

Then

1,000<em>x</em> = 2,732.343434…

and

100,000<em>x</em> = 273,234.343434…

Subtracting these makes the fractional part go away, leaving you with

100,000<em>x</em> - 1,000<em>x</em> = 273,234.343434… - 2,732.343434…

100,000<em>x</em> - 1,000<em>x</em> = 273,234 - 2,732

99,000<em>x</em> = 270,502

<em>x</em> = 270,502/99,000 = 135,251/49,500

which is clearly a rational number.

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