Question

How do you convert .15625 into a percent and fraction?

Answer 1

As a fraction`" ->15625/100000`

As a percentage`" "-> 15.625/100 -> 15.625%`

Explanation:

`color(blue)("Building the fraction")`

I am going to build the fraction in steps to emphasis what the decimal places are. In each step I keep the decimal where it is but 'slide' the number to the left by 1 place. To maintain the 'true' value I have to divide by 10 in each instance. The tens accumulate.

`"Step 1 "->0.15625/1`

`"Step 2 "->1.5625/10`

`"Step 3 "->15.625/100`

`"Step 4 "->156.25/1000`

`"Step 5 "->1562.5/10000`

`"Step 6 "->15625/100000" "larr" you now have your fraction"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Building the percentage using mathematical manipulation")`

Starting point `15625/100000`

The standard form of percent is either as `x%" or "x/100`

Change the denominator into 100 but complying with: what you do to the 'bottom' you also do to the 'top'

`(15625-:1000)/(100000-:1000) = 15.625/100 -> 15.625%`

`color(red)("Now look back at step 3")`