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How do you convert 0.135 (135 being repeated) to a fraction?

Answer 1

Nathan Axel

#5/37#

We first let 0.135 be #x#.

Since #x# is recurring in 3 decimal places, we multiply it by 1000.

#1000x = 135.135#

We then deduct them.

#1000x - x = 135.135 - 0.135#

#999x = 135#

Lastly, we divide both sides by 999 to get #x# as a fraction.

#x = 135/999#

#= 5/37#

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Answer 2

Isaiah Anthony

To convert 0.135 (repeating) to a fraction, you can use the following steps:

Let x = 0.135 (repeating).
Multiply x by 1000 to move the decimal point three places to the right: 1000x = 135.135 (repeating).
Subtract x from 1000x: 1000x - x = 135.135 (repeating) - 0.135 (repeating) = 135.
Solve for x: 999x = 135.
Divide both sides by 999: x = 135 / 999.

Therefore, 0.135 (repeating) is equal to 135/999 when expressed as a fraction in simplest form.

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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.