Question #6b526

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Question #6b526

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Answer 1 · 2017-03-19T17:14:40

$\frac{55.05}{362.48} \approx 15.19 %$ $55.05/362.48~~15.19%$ 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 $\frac{1}{100}$ $1/100$ . So, as an example:

$30 % \to 30 \times % \to 30 \times \frac{1}{100} = \frac{30}{100}$ $30% ->30xx%->30xx1/100=30/100$
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Let the unknown number be $x$ $x$

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

As we need to convert this to percentage we have:

$\frac{55.05}{362.48} = \frac{some number}{100} = \frac{x}{100}$ $55.05/362.48 = ("some number")/100 = x/100$

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

Multiply both sides by $100$ $color(red)(100)$

$\frac{55.05}{362.48} \times 100 = \frac{x}{100} \times 100$ $color(green)(55.05/362.48color(red)(xx100)" " =" " x/100color(red)(xx100))$

$\frac{55.05}{362.48} \times 100 = x \times \frac{100}{100}$ $color(green)(55.05/362.48color(red)(xx100)" " =" " x xxcolor(red)(100)/100)$

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

$\frac{55.05}{362.48} \times 100 = x$ $color(green)(55.05/362.48color(red)(xx100)" " =" " x)$

$x=15.1870.....$ 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 $~~$ means 'approximately equal to'

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Question #6b526

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