Question

What is the decimal equivalent of the octal number $217$?
A. $140$
B. $143$
C. $150$
D. $155$

Answer 1

Hint: Since the problem is based on Octal Number System hence, to convert an octal number to its decimal equivalent, the number needs to be expanded to the base of eight with its positional weight and the resulting number will be the decimal equivalent of given octal number, therefore, use the required steps to get a solution of the given problem.

Formula used:
The steps used to convert an octal number to a decimal number are: -
i. Write the octal number that needs to be converted.
ii. Multiply every digit of the octal number by the corresponding power of eight.
iii. Solve the exponents.
iv. Write the total of written numbers in the previous step

Complete step by step Solution:
 The given Octal Number is $217$.
To convert it into a decimal number, follow the below-given steps: -
i. Write the octal number that needs to be converted.
$ = 217$
ii. Multiply every digit of the octal number by the corresponding power of eight.
$ = 2 \times {\left( 8 \right)^2} + 1 \times {\left( 8 \right)^1} + 7 \times {\left( 8 \right)^0}$
iii. Solve the exponents.
$ = 2 \times 64 + 1 \times 8 + 7 \times 1$ $\left( {\therefore {a^0} = 1} \right)$
iv. Write the total of written numbers in the previous step
$ = 128 + 8 + 7 = 143$
Thus, the decimal equivalent of the octal number $217$ is $143$.

Therefore, the correct option is B.

Note: In this problem, first we have to solve or expand the question in simple form and since the number is octal, therefore, we have to use the base $8$ to convert it into decimal. Apply the required steps in a subsequent manner (as specified) to get an accurate solution to the problem. Also, it is advised to use this method only in the conversion from octal to decimal.