How do you convert #0.18bar(3)# to a fraction?

2 Answers
Dec 20, 2017

#183/1000#

Explanation:

To convert a decimal to a fraction, you have to see how many places the decimal is. This chart may help:https://www.math-salamanders.com/decimal-place-value-chart.html

After you know what place the decimal ends at, you put the numbers after the decimal point over the place. For example, your decimal #0.1bar83# repeating ends in the thousandths place, so you would put #183# over #1000#. If you had #0.47#, you can see that it ends in the hundredths place, so you would put #47# over #100#.

If you were to have a full number with your decimal, it would stay a whole number in you fraction. For example, say I had #500.678#. I would write it as a decimal as #500 678/1000#, then you would put it in simplest form: #500 439/500#.

Your number is already in simplest form, but if you were to need to put a number in simplest form, you have to get the number to where the numerator and the denominator have no more common factors.

So: #1/3# is in simplest form because one and three have no common factors but,
#2/4# is not because two and four still share the factor of two.

I hope this makes sense. If you need more information on common factors and simplest form, go to

Common Factors

or

Simplest Form

Dec 20, 2017

#0.18bar(3) = 11/60#

Explanation:

Given:

#0.18bar(3)#

Multiply by #100(10-1)# to get an integer...

#100(10-1) 0.18bar(3) = 183.bar(3)-18.bar(3) = 165#

Divide both ends by #100(10-1)# and simplify...

#0.18bar(3) = 165/(100(10-1)) = (11*color(red)(cancel(color(black)(15))))/(60*color(red)(cancel(color(black)(15)))) = 11/60#

Why #100(10-1)# ?

The first multiplier #100# shifts the given number two places to the left, so the repeating portion starts just after the decimal point. The #10# multipler shifts it one further place to the left (the length of the repeating pattern), then the #-1# subtracts the original to cancel the repeating tail.