How do you find the percent change if original: 124 tons and new: 137 tons?

1 Answer
Nov 10, 2015

Answer:

#10.58387 %# I have also explained why people say "multiply by 100".

Explanation:

The use of the word 'change' indicates that the obtained figure is compared against is the original weight. Change is 'difference' so we have:

#color(blue)("difference is 137 - 124 = 13 tons.")#
#color(brown)("Always remember to use the units of measurement.")# It is good practice, gains you marks and becomes very important when dealing with more complex calculations.

We need to compare this against something so we use the original weight. That is, a proportion of the original weight expressed as

#color(white)(xxxxxxxx )13/124#. This is 13 for 124 parts!

#color(green)(.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~)#

#color(blue)("I am now going to show you something really cool!!!")#
But this is a ratio comparing to 124 parts. We need the ratio compared to 100 parts. So I am now going to show you #color(red)("why")# people say multiply by 100. #color(brown)("A number of people will only know this as a shortcut without")#
#color(brown)("fully understanding what it is actually doing.")#

If we do this: #" "(13 divide 124)/(124 divide 124) = (0.1048387....)/1 "for 1 part"#

That is:#color(white)(xxxxxxxxxxxx)(0.1048387..."parts".)/(1 " part")#

But we need 'for 100 parts. So we now do this:

#(0.1048387....times 100)/(1 times 100) = (10.48387..)/100 =10.58387 %#

which is to 5 decimal places ( 5dp).

#color(green)(.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~)#
#color(red)("Shortcut method")#

#color(red)( 13/124 times 100 = 10.584 %color(white)(xxxx) #to 3dp