# Question 6b526

Mar 19, 2017

55.05/362.48~~15.19% to 2 decimal places

#### Explanation:

Percentage is a fraction but one were the denominator is always 100

The % symbol is a bit like a unit of measurement but one that is worth $\frac{1}{100}$ . So, as an example:

30% ->30xx%->30xx1/100=30/100
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Let the unknown number be $x$

As percentage is a fraction it makes sense to present the number in the question as a fraction as well. So we have: $\frac{55.05}{362.48}$

As we need to convert this to percentage we have:

$\frac{55.05}{362.48} = \frac{\text{some number}}{100} = \frac{x}{100}$

$\frac{55.05}{362.48} = \frac{x}{100}$

Multiply both sides by $\textcolor{red}{100}$

$\textcolor{g r e e n}{\frac{55.05}{362.48} \textcolor{red}{\times 100} \text{ " =" } \frac{x}{100} \textcolor{red}{\times 100}}$

$\textcolor{g r e e n}{\frac{55.05}{362.48} \textcolor{red}{\times 100} \text{ " =" } x \times \frac{\textcolor{red}{100}}{100}}$

But $\frac{100}{100} = 1$ giving

$\textcolor{g r e e n}{\frac{55.05}{362.48} \textcolor{red}{\times 100} \text{ " =" } x}$

$x = 15.1870 \ldots . .$ The dots indicates that the digits continue on
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But this is x/100-> x xx1/100 -> x%

so we write

55.05/362.48~~15.19%# to 2 decimal places

The $\approx$ means 'approximately equal to'