Question

How do you convert `3 3/ 8` to a decimal and a percentage?

Answer 1

divide 3 by 8 to change to a decimal and then move the decimal two places to the left to change the decimal to a percentage

Explanation:

`3/8 = .375`

`3 3/8 = 3.375`

to change to a percent move the decimal two places to the left.

# 3.375 = 337.5%

Answer 2

Suppose you do not have a calculator and you not being happy about converting `3 3/8` to decimals by direct division.

Ans `->3.375`

Explanation:

`color(blue)("The quick way")`

split `3 3/8` into `3+3/8`

Working out the `3/8` part.

Remembering that `1/8 = 0.125`

So `3/8-> 3xx0.125`

`0.125`
`ul(color(white)(0)xx3)`
`0.300" "larr" "3xx0.1`
`0.060" "larr" "3xx0.02`
`ul(0.015" "larr" "3xx0.005 larr" add them all up")`
`0.375`

Putting it all together: `3+0.375=3.375`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("One of the longer ways")`

To divide by 10 and 2 is very straight forward. So lets change the denominator such that it is a multiple of 10 and 2 to see what happens.

The first positive count of 10's for which 8 is a factor is `5xx8=40`

Considering just the `3/8`

`" "color(green)(3/8color(red)(xx1) " "->" " 3/8color(red)(xx5/5)" "=" "15/40`

This is the same as:`" "=" "15/(2xx2xx10)`

First divide by the 10 `" "=" "1.5/(2xx2)`

Second divide by one of the 2's`" "=" "0.75/(2)`

Third divide by the last 2`" "=0.375`

Putting it all together gives `3.375`