How do you convert 21.7% to a fraction in lowest terms?

Nov 10, 2016

I have deliberately gone the long way round to demonstrate a method that you can use on more complex questions. It is not really needed for this question.

$\frac{217}{1000}$

Explanation:

Note that 21.7% is the same as $\frac{21.7}{100}$

Write as: $\text{ "1/100xx21.7 " ...............Expression(1)}$

Lets get rid of the decimal

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way a number looks without changing its actual value.

$\text{ } \textcolor{b l u e}{\left[\textcolor{w h i t e}{\frac{.}{.}} 21.7 \textcolor{m a \ge n t a}{\times 1}\right] \to \left[21.7 \textcolor{m a \ge n t a}{\times \frac{10}{10}}\right] = 271 \times \frac{1}{10}}$

So write Expression(1) as:

$\text{ } \frac{1}{100} \times 217 \times \frac{1}{10}$
$\textcolor{w h i t e}{.}$

$\text{ } \frac{217}{1000}$