Question

5. Evaluate and express the result as a rational number :

(d) $\mathbf{3}\mathbf{.}\mathbf{9}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{8}\mathbf{÷}\mathbf{1000}$

Answer 1

Step 1:

For evaluation, $3.9\times 0.8÷1000$ we must use BODMAS according to which we first have to divide, i.e. $3.9\times \frac{0.8}{1000}=3.9\times 0.0008=0.00312$

Now we have to convert $0.00312$ in $\frac{p}{q}$ form.

Step 2:

$0.00312=$$0$ tenths$+0$ hundredths $+3$ thousandths $+1$ ten thousandths $+2$ hundred-thousandths$=0\times \frac{1}{10}+0\times \frac{1}{100}+3\times \frac{1}{1000}+1\times \frac{1}{10000}+2\times \frac{1}{100000}=0+0+\frac{3}{1000}+\frac{1}{10000}+\frac{2}{100000}$

$\frac{3}{1000}+\frac{1}{10000}+\frac{2}{100000}=\frac{300}{100000}+\frac{10}{100000}+\frac{2}{100000}=\frac{300+10+2}{100000}=\frac{312}{100000}$

$\frac{312}{100000}$ gets reduced to $\frac{39}{12500}$

Answer : $\frac{\mathbf{39}}{\mathbf{12500}}$