How do you convert 0.916 (6 repeating) to a fraction?
2 Answers
Explanation:
In case you have not encountered it, you can indicate a repeating sequence of digits in a decimal expansion by placing a bar over it.
So:
#0.91666... = 0.91bar(6)#
Method 1
Multiply by
#(1000-100) 0.91bar(6) = 916.bar(6) - 91.bar(6) = 825#
Divide both ends by
#0.91bar(6) = 825/(1000-100) = 825/900 = (color(red)(cancel(color(black)(75)))*11)/(color(red)(cancel(color(black)(75)))*12) = 11/12#
Why
The factor
Method 2
Given:
#0.91bar(6)#
Recognise the repeating
#color(blue)(3) * 0.91bar(6) = 2.75#
Notice that
#color(blue)(2) * 2.75 = 5.5#
Notice that
#color(blue)(2) * 5.5 = 11#
Having arrived at an integer, we can divide by the numbers we multiplied by to get a fraction:
#0.91bar(6) = 11/(2*2*3) = 11/12#
Explanation:
Given
Let
Then
Also
So:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
But
Divide both sides by 900