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How do you convert 0.036 (36 being repeated) to a fraction?

Answer 1

Eva Abramson

#4/110#

We let 0.036 be #x#.

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

#100x = 3.636#

We then deduct them.

#100x - x = 3.636 - 0.036#

#99x = 3.6#

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

#x = 3.6/99#

#= 36/990#

#= 4/110#

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Answer 2

Genesis Allen

To convert 0.036 (36 being repeated) to a fraction, you can set it as ( x = 0.0363636...), subtract the non-repeating part from the repeating part to get ( 1000x - 10x = 36 - 0.036 = 35.964 ), then solve for ( x ) to get ( x = \frac{35964}{990000} ). Simplifying the fraction gives ( x = \frac{3996}{110000} ).

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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.