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42 votes
42 votes
Is 2.73234(34 repeating) rational or irrational?

User Suneesh Ambatt
by
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1 Answer

15 votes
15 votes

It's rational because of the repeating digits.

We have

x = 2.732343434

Then

1,000x = 2,732.343434…

and

100,000x = 273,234.343434…

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

100,000x - 1,000x = 273,234.343434… - 2,732.343434…

100,000x - 1,000x = 273,234 - 2,732

99,000x = 270,502

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

which is clearly a rational number.

User Humayoon Siddique
by
2.6k points