# What is 0.004 written as a fraction of a percent?

Aug 5, 2018

$\frac{0.4}{100}$

#### Explanation:

$\textcolor{b l u e}{\text{Use of wording is critical}}$

Note that in mathematics the word 'of ' is interpreted as multiply. Also the letter 'a' (as a word) is interpreted as 1 of $\to 1 \times$

$\textcolor{b r o w n}{\underline{\text{I am convinced this is NOT what you meant!}}}$

A percent $\to \frac{1}{100}$

Let the fraction be $x$

$\text{ Fraction" color(white)("d")" of "color(white)("d")"a percent}$
$\textcolor{w h i t e}{\text{ddd")xcolor(white)("dddd.d")" of "color(white)("dd}} \frac{1}{100}$

$\textcolor{w h i t e}{\text{ddd")x color(white)("dddddd")xx color(white)("ddd}} \frac{1}{100} \equiv 0.004$
$\textcolor{w h i t e}{\text{ddddddddddddddddddd}} \uparrow$
$\textcolor{w h i t e}{\text{ddddddddddddddd")obrace("equivalent to}}$

$x = 100 \times 0.004 = 0.4 \to \frac{4}{10} \textcolor{b r o w n}{\text{ ???????}}$

$\text{ Fraction" color(white)("d")" of "color(white)("d")"a percent}$

$\textcolor{w h i t e}{\text{dddd")4/10 color(white)("dddd")xxcolor(white)("dddd")1/100color(white)("ddd}} \equiv 0.004$

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$\textcolor{b l u e}{\text{Did you mean: in the fraction format of percentage?}}$

$0.004 \equiv \frac{4}{1000}$

But we need the percentage form of this where the denominator is 100.

 (4-:10)/(1000-:10) -= 0.4/100