Question

Express each of the following decimals in the form $\frac{p}{q}$ :

$\left(i\right)0.39$

$\left(ii\right)0.750$

$\left(iii\right)2.15$

$\left(iv\right)7.010$

$\left(v\right)9.90$

$\left(vi\right)1.0001$

Answer 1

$\left(i\right)0.39$

Here, the number of decimals are $2$. So multiply by $\frac{100}{100}$.

$0.39=0.39\times \frac{100}{100}$

$=\frac{39}{100}$ [Shifting decimal for two places towards right]

$\therefore 0.39=\frac{39}{100}$

$\left(ii\right)0.750$

$0.750=0.75$

Here, the number of decimals are $2$. So multiply by $\frac{100}{100}$.

$0.75=0.75\times \frac{100}{100}$

$=\frac{75}{100}$ [Shifting decimal for two places towards right]

$=\frac{3}{4}$

$\therefore 0.750=\frac{3}{4}$

$\left(iii\right)2.15$

Here, the number of decimals are $2$. So multiply by $\frac{100}{100}$.

$2.15=2.15\times \frac{100}{100}$

$=\frac{215}{100}$ [Shifting decimal for two places towards right]

$=\frac{43}{20}$

$\therefore 2.15=\frac{43}{20}$

$\left(iv\right)7.010$

$7.010=7.01$

Here, the number of decimals are $2$. So multiply by $\frac{100}{100}$.

$7.01=7.01\times \frac{100}{100}$

$=\frac{701}{100}$ [Shifting decimal for two places towards right]

$\therefore 7.01=\frac{701}{100}$

$\left(v\right)9.90$

$9.90=9.9$

Here, the number of decimals are $1$. So multiply by $\frac{10}{10}$.

$9.9=9.9\times \frac{10}{10}$

$=\frac{99}{10}$ [Shifting decimal for one place towards right]

$\therefore 9.90=\frac{99}{10}$

$\left(vi\right)1.0001$

Here, the number of decimals are $4$. So multiply by $\frac{10000}{10000}$.

$1.0001=1.0001\times \frac{10000}{10000}$

$=\frac{10001}{100}$ [Shifting decimal for four places towards right]

$\therefore 1.0001=\frac{10001}{10000}$