How do you express #475%# as a decimal and as a mixed number or fraction in the simplest form?

1 Answer
Nov 13, 2017

Decimal : #4.75#

Fraction : #475/100 -> 1 9/4#

Explanation:

When converting a percentage to a decimal, here are two ways you can use:

#color(orange)1)# To convert #475%# to a decimal, first put 475 over one hundred:

#475/100#

*Remember that a percentage is "out of 100".

Next, simplify #475/100# to it's simplest form. They both can be divisible by 25, so:

#(25*19)/(25*4)# = #(cancelcolor(red)25*19)/(cancelcolor(red)25*4)#

= #19/4#

Convert the fraction to a decimal by dividing the numerator by the denominator. Then you get #4.75.#
#color(blue)( ........................)#

#color(green)2) # Another way you could convert #475%# to a decimal, is dividing it by one hundred. Just like before, we'll put #475# over one hundred,

#475/100#

Next we'll divide. Now an easier way to do this is to move the decimal point behind 475, to the left two space. Why two? Because there are 2 zeros in 100. Since we are dividing 475, 475 will be getting smaller. Not larger.

  • Remember, the decimal point of 475 is behind the 5. The last digit of the number.

#475-: 100 = 475. -: 100#

= 4.75
Move the decimal point to the left two spaces, thus becomes 4.75.
#color(pink)(.................................................................................................)#
#color(pink)(.................................................................................................)#

To convert #475%# to a fraction, we've already done that. :D Look above and see that in the beginning, we've found the fraction form of 475%. Lets refresh:

To convert #475%# to a fraction, first put 475 over one hundred:

#475/100#

*Remember that a percentage is "out of 100".

Next, simplify #475/100# to it's simplest form. They both can be divisible by 25, so:

#(25*19)/(25*4)# = #(cancelcolor(red)25*19)/(cancelcolor()25*4)#

= #19/4#

So, #475%# as a decimal is #4.75#, and as a fraction is #19/4# in simplest form.