Q6. - Algebra 1

Question

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

2.5%

Step-by-Step Solution

Answer

The simplest form of 2.5% is $\frac{1}{40}$.

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.

$2.5\%=\frac{2.5}{100} \left[\mathrm{Bydefinitionofpercent}\right]$

Step 3. Evaluate the expression.

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

$$\begin{gathered} 2.5\%=\frac{2.5}{100} \\ =\frac{2.5\times 10}{100\times 10} \left[\mathrm{multiplyN}\&\mathrm{Dby}10\mathrm{forremovingdecimal}\right] \\ =\frac{25}{1000} \\ =\frac{25}{25·40} \left[\mathrm{multiplyN}\&\mathrm{Dbycommonfactor}25\right] \\ =\frac{\frac{25}{25}}{\frac{25}{25}·40} \\ =\frac{1}{1·40} \\ =\frac{1}{40} \end{gathered}$$