Question

What is $\dfrac{9}{16}$ as a decimal?

Answer 1

Hint: To find the decimal of $\dfrac{9}{16}$ , we have to write 9 on the right side and 16 on the left side. Then, we have to choose the multiples of 16 that are less than (by a small amount) or equal to the dividend. . We will write the multiple below 9 and subtract it from 9. The result will be the remainder. The multiplier will be written above as quotient. We will then take the next digit of the dividend. If there is no more digit and the remainder is non-zero, then we have a decimal point after the dividend which is followed by a zero. Then we will perform the previous steps and the quotient will be written after a decimal point. We will perform these steps till the remainder becomes 0.

Complete step by step solution:
We have to find the decimal of $\dfrac{9}{16}$ . For this, we have to divide 9 by 16. The dividend is 9 and the divisor is 16. Let us write 9 on the right and 16 on the left in the following manner.
$16\overset{{}}{\overline{\left){9}\right.}}$
Let us divide 9 by 16. We have to choose the multiples of 16 that are less than (by a small amount) or equal to the dividend (9). We can see that the dividend is less than the divisor. 9 cannot be the multiple of 16. Hence, the multiple of 16 that is less than 9 will be $16\times 0=0$ . We will write the multiple 0 below 9 and subtract it from 9. The result will be the remainder. The multiplier 0, is written above as quotient.
$16\overset{0}{\overline{\left){\begin{align}
  & 9 \\
 & -0 \\
 & \_\_\_\_ \\
 & 9 \\
\end{align}}\right.}}$
We can see that the remainder is not zero and we do not have any more digits in the dividend. Hence, we have to add zeroes. If we add a zero, then we have to add a decimal point before it. Hence we can write the dividend as 9.0.
$16\overset{0}{\overline{\left){\begin{align}
  & 9.0 \\
 & -0 \\
 & \_\_\_\_ \\
 & 9 \\
\end{align}}\right.}}$
We have to bring 0 down to the remainder. Hence, the new dividend will be 90.
\[16\overset{0}{\overline{\left){\begin{align}
  & 9.0 \\
 & -0 \\
 & \_\_\_\_ \\
 & 90 \\
\end{align}}\right.}}\]
We know that $16\times 5=80<90$ . Hence, we will subtract 80 from 90 and 5 will join the quotient with a decimal point before 5.
\[16\overset{0.5}{\overline{\left){\begin{align}
  & 9.0 \\
 & -0 \\
 & \_\_\_\_ \\
 & 90 \\
 & -80 \\
 & \_\_\_\_ \\
 & \text{ }10 \\
\end{align}}\right.}}\]
Now, we will add a 0 to the dividend since the remainder is non-zero.
\[16\overset{0.5}{\overline{\left){\begin{align}
  & 9.00 \\
 & -0 \\
 & \_\_\_\_ \\
 & 90 \\
 & -80 \\
 & \_\_\_\_ \\
 & \text{ }100 \\
\end{align}}\right.}}\]
We know that $16\times 6=96<100$ . Hence, we will subtract 96 from 100 and 6 will join the quotient.
\[16\overset{0.56}{\overline{\left){\begin{align}
  & 9.00 \\
 & -0 \\
 & \_\_\_\_ \\
 & 90 \\
 & -80 \\
 & \_\_\_\_ \\
 & \text{ }100 \\
 & -96 \\
 & \_\_\_\_\_ \\
 & \begin{matrix}
   {} & 4 \\
\end{matrix} \\
\end{align}}\right.}}\]
We will repeat the steps.
\[16\overset{0.5625}{\overline{\left){\begin{align}
  & 9.0000 \\
 & -0 \\
 & \_\_\_\_ \\
 & 90 \\
 & -80 \\
 & \_\_\_\_ \\
 & \text{ }100 \\
 & -96 \\
 & \_\_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & 40 \\
\end{matrix} \\
 & \begin{matrix}
   {} & -32 \\
\end{matrix} \\
 & \_\_\_\_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & {} & 80 \\
\end{matrix} \\
 & \begin{matrix}
   {} & {} & -80 \\
\end{matrix} \\
 & \_\_\_\_\_\_\_\_\_\_ \\
 & \begin{matrix}
   {} & {} & 0 \\
\end{matrix} \\
\end{align}}\right.}}\]

Hence, the decimal value of $\dfrac{9}{16}$ is 0.5625.

Note: Students must know the terms related to division. These are dividend, divisor, quotient and remainder. Dividend is the number to be divided. Divisor will divide the dividend leaving behind a remainder. The quotient will be the number after dividing the dividend and the divisor. Students must always take for the dividend greater than the divisor. This is only applicable when the dividend is greater than or equal to the divisor. For example, if we want to divide 163 by 16, we have to first divide 16 (in 163) by the divisor 16. We should not take 1 (in 163) and divide by 16.