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How do you convert 5.23 (23 being repeated) to a fraction?

Answer 1

Genesis Allen

#518/99#

We first let 5.23 be #x#.

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

#100x = 523.23#

Next, we subtract them.

#100x - x = 523.23 - 5.23#

#99x = 518#

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

#x = 518/99#

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Answer 2

Avery Alexander

To convert 5.23 (23 being repeated) to a fraction, let x = 5.232323..., then multiply both sides by 100 to eliminate the repeating decimal: 100x = 523.232323... Subtract the original equation from the new one to eliminate the repeating decimal: 99x = 518. Solve for x to find the fraction.

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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.