Question

What is the decimal form of $\dfrac{8}{25}$

Answer 1

Hint: Divide the numerator with the denominator using the simple division. If the remainder is less than the divisor then use the decimal point in the quotient and give 10 times the remainder. Then the remainder will be greater than the divisor so that the division continues until we get ‘0’ as the remainder.

Complete step-by-step solution:
Let us assume that the required value as,
$\Rightarrow x=\dfrac{8}{25}$
Here, we can see that the dividend is 8 and the divisor is 25.
We know that the number ‘8’ is less than ‘25’ which is the divisor.
Now, let us use the decimal point in the quotient and take the dividend to its 10 times then we get
$\begin{align}
  & 25\overset{0.3}{\overline{\left){80}\right.}} \\
 & \text{ }\underline{-\left( 75 \right)\text{ }} \\
 & \text{ 5} \\
\end{align}$
Here, we can see that the remainder is ‘5’ which suggests that the division is not completed.
We know that the number ‘5’ is less than ‘25’ which is the divisor.
Here, we can see that we already used the decimal once so we can directly use the 10 times to 5.
By using the above result and continuing the division then we get,
$\begin{align}
  & 25\overset{0.32}{\overline{\left){80}\right.}} \\
 & \text{ }\underline{-\left( 75 \right)\text{ }} \\
 & \text{ 50} \\
 & \text{ }\underline{-\left( 50 \right)\text{ }} \\
 & \text{ 0} \\
\end{align}$
Here, we can see that the remainder is ‘0’ which suggests that the division is complete.
So, we can say that the required value in decimal as
$\Rightarrow x=0.32$
Therefore, the required value in decimal form is given as
$\therefore \dfrac{8}{25}=0.32$

Note: We can solve this problem in other methods also.
Let us assume that the required value as,
$\Rightarrow x=\dfrac{8}{25}$
Now, let us multiply the numerator and denominator with a number such that the denominator will be a power of 10.
Here we can see that if we multiply 25 with 4 then the denominator will be 100.
By multiplying the numerator and denominator with 4 then we get,
$\Rightarrow x=\dfrac{8\times 4}{25\times 4}=\dfrac{32.0}{100}$
We know that if the denominator is a power of 10 then the result in division will be obtained by moving the decimal point in the numerator to the power of ten numbers of places to the left.
Here, we can see that the denominator is 10 power 2 so that the result can be obtained by moving the decimal point in numerator to 2 places left side then we get,
$\Rightarrow x=0.32$
Therefore, the required value in decimal form is given as
$\therefore \dfrac{8}{25}=0.32$