Question

Convert $-\dfrac{13}{16}$ into decimal.

Answer 1

Hint: We have been given a negative fraction which we have been directed to convert to the decimal. For this, we have to divide thirteen, which is the numerator, by sixteen, which is the denominator. On dividing we will obtain a terminating decimal expansion of the fraction $\dfrac{13}{16}$. Finally, on adding a negative sign before the obtained decimal expansion, we will obtain the decimal form for the given fraction.

Complete step by step answer:
In the above question we have been given a number, which is equal to $-\dfrac{13}{16}$, and have been told to convert to the decimal. For converting it into the decimal, we consider the decimal conversion of the fraction $\dfrac{13}{16}$. For this, we divide the numerator, which is equal to thirteen, by the numerator, which is equal to sixteen. The division is shown as below.
$16\overset{0.8125}{\overline{\left){\begin{align}
  & 13 \\
 & \underline{00} \\
 & 130 \\
 & \underline{128} \\
 & 20 \\
 & \underline{16} \\
 & 40 \\
 & \underline{32} \\
 & 80 \\
 & \underline{80} \\
 & \underline{0} \\
\end{align}}\right.}}$
From the above division, we have got the decimal form for the fraction $\dfrac{13}{16}$ as $0.8125$. But since the fraction given in the above question is equal to $-\dfrac{13}{16}$, the decimal expansion of this fraction will be equal to $-0.8125$.

Hence, we have finally obtained the decimal form of the given fraction to be equal to $-0.8125$.

Note: Do not forget to add a negative sign before the decimal expansion obtained from the division of thirteen by sixteen. This is because the fraction given to us in the question is equal to $-\dfrac{13}{16}$, and not equal to $\dfrac{13}{16}$. Also, we must obtain the complete decimal expansion and not write an approximate decimal expansion.