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# Percentages

Percentages

Changing a percentage to a decimal

Divide it by 100.

Eg:
17.25% goes to
17.25/100 = 0.1725

Changing a percentage to a fraction

Times it by 1/100

Eg:
3 and 1/3% goes to
15/4% goes to
15/4 * 1/100 goes to
3/4 * 1/20 = 3/80

Changing a decimal to a percentage

Times it by 100%

Eg:
0.27 * 100% = 27%

Changing a fraction to a percentage

Divide the numerator by the denominator and times by 100%

Eg:
3/8 goes to
0.375 * 100%
= 37.5%

Finding a percentage of a quantity

Either -
press the amount * the percent amount and hit the % button
or -
change the percent to a decimal and times it by the quantity

Eg:
7 and 3/4% of 84.35 goes to
0.0775 * 84.35 = 6.54

Expressing as a percentage

percentage of an amount to an another amount.

amount a divided by amount b times 100%

Eg:
1000kg of 2000kg goes to
1000/2000 * 100%
50%

Percentage change

decrease or increase

change in value/original value * 100%

Eg decrease:
O price = 6.10
new price = 5.30
change in value = 6.1 - 5.3 = 0.8
0.8/6.1 * 100%
= 13.11%

Eg increase:
O prince = 18000
new price = 21000
change in value = 3000
3000/18000 * 100%
= 16.67%

Finding new price

increase or decrease

find the percentage, add or take to/from original price.

find original price

let the original price be x. Use algebra.

Eg:
falls 16% to \$30
x - 16% of x = 30
x - 0.16x = 30
(1 - 0.16)x = 30
0.84x = 30
0.84x/0.84 = 30/0.84
original price = \$35.71

Profit and loss

profit/cost price * 100
loss/cost price * 100

Eg:
cost price = \$125
sell price = \$165
profit = \$165 - \$125 = \$40
40/165 *100% = 24.24% profit

Nice little cheat sheet you came up with there.

Another common one you should add to the list is how to find the percentage of a number.

Ex. What is 24% of 80?
.24*80= 19.2

edit: ah, I guess you already have one similar in "Finding a percentage of a quantity". Dunno how I missed that.
Ghost Rider103 on Mon Nov 21, 2011 4:45 pm
Is it correct to say:
25% = 0.25
?

If we treat % as a variable and solve the equation we get
% = 0.01

This seems valid. Is this a common thing to do?
Peterssidan on Mon Nov 21, 2011 5:27 pm
 Peterssidan wrote: Is it correct to say: 25% = 0.25 ? If we treat % as a variable and solve the equation we get % = 0.01 This seems valid. Is this a common thing to do?

lol. nice one.

That is also because per cent means every one hundred. So yeah % = 1/100 = 0.01.
loremar on Mon Nov 21, 2011 5:36 pm
 Quote: Is it correct to say: 25% = 0.25 ?

Yep. To change a percentage into a decimal, you just put the decimal in front of the percentage. Or in mathematical terms, just divide the percentage by 100.

25/100=0.25
Ghost Rider103 on Mon Nov 21, 2011 6:26 pm
25% = 0.25 makes sense...
If you think of 100% as 1 (whole),
25% is 25/100 is 1/4 of 1 (whole)
1 divided by 4 is 0.25, 4 groups of 0.25 will make 1 (whole).

1% goes to 1/100 goes to 0.01, that makes sense.
Hello_World on Tue Nov 22, 2011 7:58 am
Well what you just said complicates things.

I understand what you mean. But for me, when learning, I like to just stick to the basics. Divide the percentage by 100 to get the decimal. Done.
Ghost Rider103 on Tue Nov 22, 2011 3:38 pm
Hmmm... that is an interesting comment.

I suppose that you are correct, it does complicate things somewhat.

But for myself, I find I retain better if I can fit things into a bigger picture in some small way.

Then if I forget the procedure, sometimes I can figure it out backwards.

It does mean that everything I try to learn seems to take longer, and that I don't understand the weirdest stuff (according to others). (Stuff which may be a simple procedure but I can't fathom why I am trying to do it in the first place..)
Hello_World on Tue Nov 22, 2011 10:37 pm