If a number in base 8 is represented as '57', what is its equivalent in base 10?

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Question: If a number in base 8 is represented as \'57\', what is its equivalent in base 10?

Options:

Correct Answer: 49

Solution:

\'57\' in base 8 = 5*8^1 + 7*8^0 = 40 + 7 = 47 in decimal.

If a number in base 8 is represented as '57', what is its equivalent in base 10?

If a number in base 8 is represented as '57', what is its equivalent in base 10?

Step 1: Understand that '57' is a number in base 8.
Step 2: Identify the digits in '57'. The first digit is 5 and the second digit is 7.
Step 3: Recognize the place values in base 8. The first digit (5) is in the '8^1' place and the second digit (7) is in the '8^0' place.
Step 4: Calculate the value of the first digit: 5 * 8^1 = 5 * 8 = 40.
Step 5: Calculate the value of the second digit: 7 * 8^0 = 7 * 1 = 7.
Step 6: Add the two values together: 40 + 7 = 47.
Step 7: Conclude that '57' in base 8 is equal to 47 in base 10.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base 8 to base 10.
Positional Notation – Recognizing the significance of each digit's position in a number system, where each position represents a power of the base.