# How to find out what a fraction is as a percentage?

• Jul 1st 2012, 09:37 AM
Subliminalmessage
How to find out what a fraction is as a percentage?
I've got six questions I've picked out of many I can't seem to get exactly right.

1/12 as a percentage = 8.4% (correct answers is 8.3%)
1/8 = 12.4% (12.5%)
1/16 = 6.4% (6.25%)
2/3 = 66.2% (66.6%)
6/16 = 36.24% (37.5%)
5/8 = 32.0% (62.5%)

So, the way I worked these out is as following, I'll show you one example of how I got these incorrect answers.

2/3, 3 divided by 100, so 3 goes into 10, 3 times remainder 1 put the 1 ontop of the second 0 and it becomes 10 and 3 goes into 10, 3 times remainder 1.

So I've got 33.1 now I times 33.1 with the top number of the fraction which is 2, 33.1 x 2 = 66.2%?

Any idea where I'm going wrong here? Thanks.
• Jul 1st 2012, 11:35 AM
biffboy
Re: How to find out what a fraction is as a percentage?
Quote:

Originally Posted by Subliminalmessage
I've got six questions I've picked out of many I can't seem to get exactly right.

1/12 as a percentage = 8.4% (correct answers is 8.3%)
1/8 = 12.4% (12.5%)
1/16 = 6.4% (6.25%)
2/3 = 66.2% (66.6%)
6/16 = 36.24% (37.5%)
5/8 = 32.0% (62.5%)

So, the way I worked these out is as following, I'll show you one example of how I got these incorrect answers.

2/3, 3 divided by 100, so 3 goes into 10, 3 times remainder 1 put the 1 ontop of the second 0 and it becomes 10 and 3 goes into 10, 3 times remainder 1.

So I've got 33.1 now I times 33.1 with the top number of the fraction which is 2, 33.1 x 2 = 66.2%?

Any idea where I'm going wrong here? Thanks.

a/b as a percentage= (a divided by b)*100
• Jul 1st 2012, 02:26 PM
BobP
Re: How to find out what a fraction is as a percentage?
$\displaystyle \frac{100}{3}=33$ remainder $\displaystyle 1,$

but that is $\displaystyle 33+\frac{1}{3}=33 + 0.333...=33.333...,$ not $33.1$
• Jul 1st 2012, 07:07 PM
HallsofIvy
Re: How to find out what a fraction is as a percentage?
Quote:

Originally Posted by Subliminalmessage
I've got six questions I've picked out of many I can't seem to get exactly right.

1/12 as a percentage = 8.4% (correct answers is 8.3%)
1/8 = 12.4% (12.5%)
1/16 = 6.4% (6.25%)
2/3 = 66.2% (66.6%)
6/16 = 36.24% (37.5%)
5/8 = 32.0% (62.5%)

So, the way I worked these out is as following, I'll show you one example of how I got these incorrect answers.

2/3, 3 divided by 100

You mean 100 divided by 3

Quote:

, so 3 goes into 10, 3 times remainder 1 put the 1 ontop of the second 0 and it becomes 10 and 3 goes into 10, 3 times remainder 1.

So I've got 33.1 now I times 33.1 with the top number of the fraction which is 2, 33.1 x 2 = 66.2%?
Yes. Another way to do this would be to divide 200 by 3, and yet another way is to divide 2 by 3, then multiply by 3.

Quote:

Any idea where I'm going wrong here? Thanks.
For that example, at least, you are not doing anything wrong.
$\frac{a}{b}$, converted to a percent, can be thought of as [tex]\frac{100}{b}[/itex], multiplied by a, or $\frac{100a}{b}$, or $\frac{a}{b}$ multilied by 100. In any case, you divide a by b and multiply by 100. Because multiplication (and division) are "commutative" the order in which you do that doesn't matter.

Quote:

1/12 as a percentage = 8.4% (correct answers is 8.3%)
12 divides into 100 8 times with remainder 4. 12 divides into 40 3 times with remainder 4 again. If you keep on you will repeatedly get "3 times with remainder 3. 12 divides into 100 8.333333333333333333333333333... which, rounded to tenths place, is 8.3%. The fact that the last remainder was "4" does NOT mean the last digit is 4!

[quote]1/8 = 12.4% (12.5%)[quote]
8 divides into 100 12 times with remainder 4. Bringing down a "0", 8 divides into 40 5 times: 8 divides into 100 12.5 times. Again, the fact that the remaider is 4 does NOT mean that the digit is 4, it means it is 4/8= 1/2= .5.

Quote:

1/16 = 6.4% (6.25%)
16 divides into 100 6 times with remainder 4. I think I see a pattern here! The remainder is NOT the last digit. 4/16= 1/4= .25.
You continue these. Remember, the "last" remaider is NOT a digit in the quotient. Your difficulty here has nothing to do with "percents"- it is with long division.

[quote]2/3 = 66.2% (66.6%)
6/16 = 36.24% (37.5%)
5/8 = 32.0% (62.5%)