Question #6b526

1 Answer
Mar 19, 2017

Answer:

#55.05/362.48~~15.19%# to 2 decimal places

Explanation:

Percentage is a fraction but one were the denominator is always 100

The % symbol is a bit like a unit of measurement but one that is worth #1/100# . So, as an example:

#30% ->30xx%->30xx1/100=30/100#
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Let the unknown number be #x#

As percentage is a fraction it makes sense to present the number in the question as a fraction as well. So we have: #55.05/362.48#

As we need to convert this to percentage we have:

#55.05/362.48 = ("some number")/100 = x/100#

#55.05/362.48 = x/100#

Multiply both sides by #color(red)(100)#

#color(green)(55.05/362.48color(red)(xx100)" " =" " x/100color(red)(xx100))#

#color(green)(55.05/362.48color(red)(xx100)" " =" " x xxcolor(red)(100)/100)#

But #100/100=1# giving

#color(green)(55.05/362.48color(red)(xx100)" " =" " x)#

#x=15.1870.....# The dots indicates that the digits continue on
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But this is #x/100-> x xx1/100 -> x%#

so we write

#55.05/362.48~~15.19%# to 2 decimal places

The #~~# means 'approximately equal to'