How do you convert 0.16 (6 repeating) to a fraction?
4 Answers
Explanation:
y = 0.16666.
Multiply by 10: 10y = 1.66666.. = 1 + 0.6666...=
Divide by 10:
Explanation:
First multiply by
The first multiplier of
#(100-10) * 0.1bar(6) = 16.bar(6) - 1.bar(6) = 15#
Then divide both ends by
#0.1bar(6) = 15/(100-10) = 15/90 = (1*color(red)(cancel(color(black)(15))))/(6*color(red)(cancel(color(black)(15)))) = 1/6#
A
Explanation:
Note: if the 6 is repeating then a way of showing this is to put a bar over the last 6 you write:
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let
Then
Also
So
Divide both sides by 90
But
Short cut methods for finding the fraction:
Explanation:
The details of how to convert a recurring decimal into a fraction are shown in the other answers.
However, sometimes you just want a quick method.
Here is the short cut.
If all the digits after the decimal point recur:
Write down the digits (without repeating) as the numerator.
Write a
If only some digits recur
Numerator: write down all the digits - non-recurring digits
Denominator: a
In