# How do you change 0.452 into a percent and how do you round it to the nearest tenth of a percent?

Oct 22, 2016

$0.452$ is 45.2%.

#### Explanation:

To change any decimal to a percent, you multiply the decimal by $100$..

0.452 * 100 = 45.2%

In order to round to the nearest tenth, you examine the value in the hundredths place to determine whether or not the number in the tenths place will be kept or rounded up. However, there is no hundredths place in this case, so you are not able to round.

Amendment:

The above method of changing a decimal to a percent is the "easily remembered" method. It is based on the combination of several properties and definitions.

First, a percent is is part of one whole unit (or item, or total, etc.). Therefore, 100% is equal to $1$.

The number $1$ is the Multiplicative Identity. Remember that the Identity Property of Multiplication states that multiplication by the Multiplicative Identity ($1$) does not change the value of the original number. Algebraically stated, this is $a \cdot 1 = a$.

Also, remember that any number has multiple forms. In this case, let's consider some equivalent forms of the number $1$.
1 = 3/3 = (x + 7)/(x + 7) = 100%
All four of these previous representations are equivalent in value. The Substitution Property of Equality allows us to use 100% in place of $1$ when applying the Identity Property of Multiplication. Therefore, multiplying a decimal by 100% does not change its value, only its form.

And so, the more correct representation of the process shown in the original explanation is:

0.452 * 100% = 45.2%

If my earlier explanation was too simplistic or mislead anyone, I apologize.

Oct 22, 2016

0.452 = 452/1000 = 45.2/100 = 45.2%

#### Explanation:

Decimals and percentages are interchangeable without any working at all. They are just different ways of writing the same thing.
Here are some examples.

25/100 = 25 " hundredths" = 25% = 0.25

Percentages are out of 100 and the second decimal place represents hundredths.

0.16 = 16/100 = 16%

7% = 7/100 = 0.07

135% = 135/100 = 1.35

4.5% = 4.5/100 = 45/1000 = 0.045

0.452 = 452/1000 = 45.2/100 = 45.2%

It is already correct to one tenth of a percent (the first place holder after the decimal point.)

Oct 23, 2016

45.2% to the nearest tenth of a percent.

#### Explanation:

Think of $0.452$ as $\text{ } 0 + \frac{4}{10} + \frac{5}{100} + \frac{2}{1000}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider the } \frac{4}{10}}$

If we multiply it by 1 but in the form of $1 = \frac{10}{10}$ we have

$\text{ "[4/10color(magenta)(xx1)]" "->" "[4/10color(magenta)(xx10/10)]" " =" } \frac{40}{100}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it back together}}$

So we can write $0.452$ as $\text{ } 0 + \frac{40}{100} + \frac{5}{100} + \frac{2}{1000}$

Which is the same as $\frac{45}{100} + \frac{2}{1000}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider the } \frac{2}{1000}}$

This can be written as $\frac{2}{100 \times 10}$ which if we cancel out gives

$\text{ } \frac{{\cancel{2}}^{0.2}}{100 \times {\cancel{10}}^{1}}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it back together}}$

So we can write $0.452$ as $\text{ "45/100+0.2/100" "=" } \frac{45.2}{100}$

$\textcolor{b r o w n}{\text{Another way of writing "1/100" is %}}$
$\textcolor{b r o w n}{\text{That way % is the unit of measurement worth } \frac{1}{100}}$

So 0.452" is equivalent to "45.2/100" " ->" " 45.2xx1/100" "->""45.2%
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that $0.2 \to \frac{2}{10}$ but this number is part of the percentage so it is already to the nearest tenth of a percent.