### Theory:

4. Conversion of ratio into percent

We can convert ratio into a percentage using the following method.
Example:
(i) $$a:b$$

$\begin{array}{l}=\frac{a}{b}\\ \\ =\left[\frac{a}{b}×100\right]%\end{array}$

(ii) $$3:8$$

$\begin{array}{l}=\frac{3}{8}\\ \\ =\left[\frac{3}{8}×100\right]%\\ \\ =37\frac{1}{2}%\end{array}$

5. Conversion of Percent into decimal
To convert the percent to decimal, first change it to a fraction by dividing it by $$1000$$ and remove the $$\%$$ sign. Then put the decimal point accordingly.
$$a\%$$           $$= a/100$$        $$= 0.0a$$
(percent)     (fraction)       (decimal)
Example:
(i) 25$$\%$$

$$=$$ $\frac{25}{100}$

$$=$$ 0.25$$\%$$

(ii) 85$$\%$$

$$=$$ $\frac{85}{100}$

$$=$$ 0.85$$\%$$

(iii) $\frac{2}{9}%$

$$=$$ $\frac{2}{9·100}$

$$=$$ 0.002$$\%$$
6. Conversion of decimal into a Percent
To convert decimal into a percent, first, change it to fraction for the removal of decimal and then multiply it by $$100$$ and put the $$\%$$ sign.
Example:
(i) 10.9

$$=$$ $\frac{109}{10}$

$$=$$ $\left[\phantom{\rule{0.147em}{0ex}}\frac{109}{10}×100\right]%$

$$=$$ 1090$$\%$$

(ii) 0.036

$$=$$ $\frac{36}{1000}$

$$=$$ $\frac{36}{1000}·100$

$$=$$ 3.6$$\%$$