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How do you convert 0.23 (23 being repeated) to a fraction?

Answer 1

Abigail Allen

#23/99#

We first let 0.23 be #x#.

Since #x# is recurring in 2 decimal places, we multiply it by 100.

#100x = 23.23#

Next, we subtract them.

#100x - x = 23.23 - 0.23#

#99x = 23#

Lastly, we divide both sides by 99 to get #x# as a fraction.

#x = 23/99#

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Answer 2

Eva Adamson

To convert 0.23 (repeating) to a fraction, let x = 0.23 (repeating): 100x = 23.2323... 10x = 2.3232...

Subtract the second equation from the first: 90x = 21

Divide both sides by 90: x = 21/90

Simplify the fraction: x = 7/30

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.