Question

Express the following percent as a fraction or mixed number in the simplest form.

0.4%

Short answer

The simplest form of 0.4% is $\frac{1}{250}$.

Step-by-step solution

Step 1. Concept of Percentage.

Percent of a number is defined as the ratio of the number and 100.

Step 2. Find the percent of given numbers.

$0.4\%=\frac{0.4}{100} \left[\mathrm{Bydefinitionofpercent}\right]$

Step 3. Evaluate the expression.

First, remove decimal from the numerator and then cancel out the common factor from numerator and denominator.

$$\begin{gathered} 0.4\%=\frac{0.4}{100} \\ =\frac{0.4\times 10}{100\times 10} \left[\mathrm{multiplyN}\&\mathrm{Dby}10\mathrm{forremovingdecimal}\right] \\ =\frac{4}{1000} \\ =\frac{4}{4·250} \left[\mathrm{multiplyN}\&\mathrm{Dbycommonfactor}4\right] \\ =\frac{\frac{4}{4}}{\frac{4}{4}·250} \\ =\frac{1}{1·250} \\ =\frac{1}{250} \end{gathered}$$