### Theory:

4. Conversion of ratio into per cent

We can convert the 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 per cent into decimal
To convert the per cent to decimal, first change it to a fraction by dividing it by $$1000$$ and remove the $$\%$$ sign. Then put the decimal point accordingly.
$$a\%$$           $$= a/100$$        $$= 0.0a$$
(per cent)     (fraction)       (decimal)
Example:
(i) 35$$\%$$

$$=$$ $\frac{35}{100}$

$$=$$ 0.35

(ii) 87$$\%$$

$$=$$ $\frac{87}{100}$

$$=$$ 0.87

(iii) $\frac{1}{8}%$

$$=$$ $\frac{1}{8·100}$

$$=$$ 0.001

6. Conversion of decimal into a per cent
To convert decimal into a per cent, change it to fraction to remove decimal and then multiply it by $$100$$ and put the $$\%$$ sign.
Example:
(i) 5.6

$$=$$ $\frac{56}{10}$

$$=$$ $\left[\phantom{\rule{0.147em}{0ex}}\frac{56}{10}×100\right]%$

$$=$$ 560$$\%$$

(ii) 0.035

$$=$$ $\frac{35}{1000}$

$$=$$ $\left[\phantom{\rule{0.147em}{0ex}}\frac{35}{1000}×100\right]%$

$$=$$ 3.5$$\%$$