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In a base 8 system, what is the value of '57'?

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Question: In a base 8 system, what is the value of \'57\'?

Options:

  1. 45
  2. 46
  3. 47
  4. 48

Correct Answer: 46

Solution: 

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

In a base 8 system, what is the value of '57'?

Practice Questions

Q1
In a base 8 system, what is the value of '57'?
  1. 45
  2. 46
  3. 47
  4. 48

Questions & Step-by-Step Solutions

In a base 8 system, what is the value of '57'?
  • Step 1: Understand that '57' is in base 8. This means each digit represents a power of 8.
  • Step 2: Identify the digits in '57'. The first digit is '5' and the second digit is '7'.
  • Step 3: Determine the place values. 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 decimal.
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