# Express each of the following decimals in the form

Question:

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

(i) $0.39$

(ii) $0.750$

(iii) $2.15$

(iv) $7.010$

(v) $9.90$

(vi) $1.0001$

Solution:

(i) Given decimal is $0.39$

Now we have to convert given decimal number into the $\frac{p}{q}$ form

Let $\frac{p}{q}=0.39$

$\Rightarrow \frac{p}{q}=\frac{39}{100}$

(ii) Given decimal is $0.750$

Now we have to convert given decimal number into $\frac{p}{q}$ form

Let $\frac{p}{q}=0.750$

$\Rightarrow \frac{p}{q}=\frac{750}{1000}$

$\Rightarrow \frac{p}{q}=\frac{75}{100}$

$\Rightarrow \frac{p}{q}=\frac{3}{4}$

(iii) Given decimal is $2.15$

Now we have to express the given decimal number into $\frac{p}{q}$ form

Let $\frac{p}{q}=2.15$

$\Rightarrow \frac{p}{q}=\frac{215}{100}$

$\Rightarrow \frac{p}{q}=\frac{43}{20}$

(iv) Given decimal is $7.010$

Now we have to express the given decimal number into $\frac{p}{q}$ form

Let $\frac{p}{q}=7.010$

$\Rightarrow \frac{p}{q}=\frac{7010}{1000}$

$\Rightarrow \frac{p}{q}=\frac{701}{100}$

(v) Given decimal is $9.90$

Now we have to find given decimal number into $\frac{p}{q}$ form

Let $\frac{p}{q}=9.90$

$\Rightarrow \frac{p}{q}=\frac{990}{100}$

$\Rightarrow \frac{p}{q}=\frac{99}{10}$

Hence, $9.90=\frac{99}{10}$

(vi) Given decimal is $1.0001$

Now we have to find given decimal number into $\frac{p}{q}$ form

$\frac{p}{q}=1.0001 \Rightarrow \frac{p}{q}=\frac{10001}{10000}$