Question

Solve the following: $0.4÷20$.

Answer 1

Hint: First we need to express the decimal form into fractional form. To convert a decimal into a fraction we first write the number in the numerator and put $1$ in the denominator. Then we multiply both the numerator and denominator by $10$ for every digit after the decimal point. Dividing the first number by the second number is the same as multiplying the first number by the reciprocal of the second number.

Complete step-by-step answer:
So we are given that the answer of $0.4÷20$ is $0.02$. We need to find the correctness of the statement.
So we first convert the decimal $0.4$ into a fraction. So here we have one digit after the decimal point so we need to multiply both numerator and denominator by $10$.
The fractional form of $0.4$ is
$0.4={\displaystyle \frac{0.4}{1}}$
$\Rightarrow 0.4={\displaystyle \frac{0.4\times 10}{1\times 10}}$
$\Rightarrow 0.4={\displaystyle \frac{4}{10}}$
Now we have to perform the division so we have to multiply the first term by the reciprocal of the second term.
$\therefore$ The reciprocal of the second term $20$ is ${\displaystyle \frac{1}{20}}$.
Thus we get:
$0.4÷20$
$={\displaystyle \frac{4}{10}}\times {\displaystyle \frac{1}{20}}$
$={\displaystyle \frac{4}{200}}$
We have $2$ in both numerator and denominator.
So, dividing both numerator and denominator by $2$ we get:
$={\displaystyle \frac{2\times 2}{2\times 100}}$
$={\displaystyle \frac{2}{100}}$
$=0.02$
To convert the fraction into decimal we place the decimal point two places left of the digit in the numerator.

Note: One should be well acquainted with the conversion of decimal into a fraction and vice versa to conduct all the operations. One should take note that in the case of division of fractions we always multiply the reciprocal of the divisor. So, we should be careful in finding the reciprocal of a number.