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

1 Answer
May 21, 2016

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")#