Question

The representation of octal number ${(532.2)}_8$ in decimal is

Answer 1

Step 1: Definition of octal number system

Octal number system:

A number system that has its base as $8$ is called an octal number system.

The numbers in this number system are formed using the digits $0$ to $7$

Step 2: Represent the given octal number in decimal

$$\begin{gathered} \Rightarrow {\left(532.2\right)}_8=\left(5\times 8^2\right)+\left(3\times 8\right)+\left(2\times 8^0\right)+\left(2\times 8^{-1}\right) \\ \Rightarrow {\left(532.2\right)}_8=\left(320\right)+\left(24\right)+\left(2\right)+\left(\frac{2}{8}\right) \\ \Rightarrow {\left(532.2\right)}_8=346+\left(0.25\right) \\ \Rightarrow {\left(532.2\right)}_8=346.25 \end{gathered}$$

Hence the required answer is $346.25$