How do you convert 0.83 (3 repeating) to a fraction?
2 Answers
Explanation:
To format this question type you write: 0.8bar3
But you use the hash key just before 0.8bar3
and also at the end. So you end up with
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let
Then
So
Multiply both sides by 10
Divide both sides by 90
Here's a method using a calculator to help...
Explanation:
Here's another way you can convert decimals to fractions if you have a calculator to hand.
We use the calculator to find the terminating continued fraction expansion for the given number, then unwrap it to a regular fraction.
For our example, type
Note that the portion before the decimal point is
#color(blue)(0) + #
Take the reciprocal of the given number to get a result something like:
#color(blue)(0) + 1/color(blue)(1)#
then subtract it to get
#color(blue)(0) + 1/(color(blue)(1)+1/color(blue)(5)) = 0+1/(6/5) = 5/6#
Another example
Just to make the method a little clearer, let us consider a more complex example:
Given:
#3.82857142857#
Note the
#1.20689655173#
Note the
#4.83333333320" "color(lightgrey)"Note the rounding error"#
Note the
#1.20000000019#
Note the
#4.99999999525#
Let's call that
Taking the numbers we have found, we have:
#3.82857142857 = color(blue)(3) + 1/(color(blue)(1)+1/(color(blue)(4)+1/(color(blue)(1)+1/color(blue)(5))))#
#color(white)(3.82857142857) = color(blue)(3) + 1/(color(blue)(1)+1/(color(blue)(4)+5/6))#
#color(white)(3.82857142857) = color(blue)(3) + 1/(color(blue)(1)+6/29)#
#color(white)(3.82857142857) = color(blue)(3) + 29/35#
#color(white)(3.82857142857) = 134/35#