# Math Help - Comparing Percents, Decimals, and Fractions

1. ## Comparing Percents, Decimals, and Fractions

I am trying to help my daughter with her homework. I cannot remember how to change percents or decimals. Sad I know?!

Her assignment is using greater than, less than, and equal. For example:

62% 5/8 I can't remember the steps to figure out which is
greater than, less than, or equal.

0.9 9% This is another kind of example.

ANY help would be appreciated. I am at a loss!

Thank You!
Hope

2. Originally Posted by Hope
I am trying to help my daughter with her homework. I cannot remember how to change percents or decimals. Sad I know?!

Her assignment is using greater than, less than, and equal. For example:

62% 5/8 I can't remember the steps to figure out which is
greater than, less than, or equal.

0.9 9% This is another kind of example.

ANY help would be appreciated. I am at a loss!

Thank You!
Hope
Percent means divided by 100.

Thus, $62 \% =\frac{62}{100}$
And,
$\frac{5}{8}$

Commond denominator is 200.

Multiply the first fraction by 2 and second 25.

$\frac{62}{100} \cdot \frac{2}{2} = \frac{128}{200}$

$\frac{5}{8} \cdot \frac{25}{25} = \frac{125}{200}$

Thus, the first one is larger.

3. Originally Posted by Hope
I am trying to help my daughter with her homework. I cannot remember how to change percents or decimals. Sad I know?!

Her assignment is using greater than, less than, and equal. For example:

62% 5/8 I can't remember the steps to figure out which is
greater than, less than, or equal.

0.9 9% This is another kind of example.

ANY help would be appreciated. I am at a loss!

Thank You!
Hope

A) To change percent to decimals:

Percent is "per century" or per hundred.
So 62% = 62/100 = 0.62
Or, as short cut, move the decimal point 2 places to the left.
In 62, the decimal point is understood to be at the end of the number, after the 2. So move the not-shown decimal point to two places to the left. Past 2, past 6, so ----0.62.

9% = 9/100 = 0.09
Or, 9. ----move the decimal point two places to the left = .09 = 0.09

B) To change decimals to percent:

Reverse the procedure mentioned above. Now it is move the decimal point two places to the right.
0.62 = 62%
0.09 = 9%
0.005 = 0.5%
1.5943 = 159.43%

To change a fraction to decimals, just divide the numerator by the denominator.
5/8 = 5 divided by 8 = 0.625
If you want that in percent, you move the decimal point to two plces to the right, thus, 0.625 = 62.5%

-----------------------------------------
Compare 62% and 5/8

You can do that in decimals. Convert both in their decimal forms.
62% = 0.62
5/8 = 0.625
Since 0.625 is greater than 0.62,
then 62% is less than 5/8
or 5/8 is greater than 62%.

----------------------------------------
0.9 and 9%

1) Say, put them in tdecimal forms.
0.9 = 0.9
9% = 0.09
So, since 0.9 is grater than 0.09 ----(0.9 is also 0.90, or 0.9000000, etc)
then, 0.9 is greater than 9%.

Or, 9% is less than 0.9

2) Say, put them in their % forms.
0.9 = 90%
9% = 9%
So, 0.9 is greater than 9%

4. Hello, Hope!

Greater than, less than, or equal?

$(1)\;62\%\text{ and }\frac{5}{8}$

$(2)\;0.9\text{ and }9\%$

As was pointed out, "percent" means "per hundred".

To change a percent to a fraction:
. . write the number over 100,
. . drop the percent sign.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

$(1)\;\;62\%\text{ and }\frac{5}{8}$

First: . $62\%\:=\:\frac{62}{100}$

Now we compare $\frac{62}{100}$ and $\frac{5}{8}$
. . . . $\frac{62}{100}\;\;\boxed{?}\;\;\frac{5}{8}$

Here's a trick you can use for comparing fractions: "cross-multiply".

We have: . $\frac{62}{100}\!\begin{array}{cc}_{\nwarrow} \\ ^{\nearrow}\end{array}\!\!\!\!\!\begin{array}{cc}_ {\nearrow} \\ ^{\nwarrow}\end{array}\!\frac{5}{8}\quad\Rightarro w\quad 62\times8 \;\;\boxed{?}\;\;100 \times 5$ . $\quad\Rightarrow\quad 496\;\;\boxed{?}\;\;500$

Since $496 < 500$, the correct sign is "less than".

Answer: . $62\%\;<\;\frac{5}{8}$

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$(2)\;\;0.9\text{ and }9\%$

First, $9\% = \frac{9}{100}$

We have: . $0.9\;\;\boxed{?}\;\;\frac{9}{100}$

Cross-multiply: . $\frac{0.9}{1}\begin{array}{cc}_{\nwarrow} \\ ^{\nearrow}\end{array}\!\!\!\!\begin{array}{cc}_{\ nearrow} \\ ^{\nwarrow}\end{array}\frac{9}{100}\quad\Rightarro w\quad 0.9 \times 100 \;\;\boxed{?}\;\;1 \times 9\quad\Rightarrow\quad 90\;\;\boxed{?}\;\;9$

Since $90 > 9$, the correct sign is "greater than".

Answer: . $0.9\;> \;9\%$