# How do you convert 4/25 into a decimal and percent?

May 7, 2017

Quite a bit of teaching about principles. The calculation should only take a few lines once you are used to these.

Percentage->16%
Decimal $\text{ } \to 0.16$

#### Explanation:

$\textcolor{b l u e}{\text{Teaching about percentage}}$

Percentage is basically a fraction. However it is a special fraction in that the bottom number is fixed at 100.

Using an example of thirty percent.
There are two ways that a percentage can and may be written.

For our example we have 30% and 30/100. These mean EXACTLY the same thing. If that is the case then we have:

$\frac{30}{100} = 30 \times \frac{1}{100}$

30% = 30xx%

If they mean exactly the same thing then % is another way of writing $\frac{1}{100}$

When using the shortcut what do they mean by: "multiply by 100 and put a % on the end" ?

Basically they are multiplying by 1 but in the form of $\frac{100}{100}$

$\text{something"xx1 color(white)("dddddddd")->color(white)("dddd")"something} \times \frac{100}{100}$

$\text{The multiply by 100 bit"color(white)("d")->color(white)("dddd")"something} \times 100 \times \frac{1}{100}$

color(white)("dddddddddddddddddd.d")->color(white)("dddd")"something"xx100xx%

color(white)("dddddddddddddddddd.d")->color(white)("dddd")"something"xx100%

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$\textcolor{b l u e}{\text{Answering the percent part of the question}}$

$\textcolor{g r e e n}{\frac{4}{25} \textcolor{red}{\times 1} \textcolor{w h i t e}{\text{dddd")->color(white)("dddd}} \frac{4}{25} \textcolor{red}{\times \frac{4}{4}}}$

color(green)(color(white)("dddddddddd")->color(white)("dddd") (4xx4)/(25xx4)

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddd")->color(white)("ddddd}} \frac{16}{100}}$

But this is the same as $16 \times \frac{1}{100}$ and $\frac{1}{100}$ is the same as %. So we have:

color(white)("dddddddddddddddd")color(green)(4/25=16%)

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$\textcolor{b l u e}{\text{The decimal part of the question}}$

$\textcolor{b r o w n}{\text{The teaching bit}}$

A decimal construct is such that we have:

units + tenths + hundredths + .....

Using an example: suppose we had the number 23.26

Units $\to 23 \text{ "larr" Units is counting in 1's}$

Tenths $\to \frac{2}{10}$

Hundredths$\to \frac{6}{100}$

$\frac{23}{1} + \frac{2}{10} + \frac{6}{100} \text{ "->" } 23.26$
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$\textcolor{b r o w n}{\text{Back to our question}}$

We have 16%->16/100

So we have: $\frac{0}{1} + \frac{1}{10} + \frac{6}{100} \text{ "->" } 0.16$