In a base 8 number system, what is the value of the number 57 in decimal?

₹0.0

Question: In a base 8 number system, what is the value of the number 57 in decimal?

Options:

Correct Answer: 47

Solution:

To convert from base 8 to decimal, calculate: 5*8^1 + 7*8^0 = 5*8 + 7*1 = 40 + 7 = 47.

In a base 8 number system, what is the value of the number 57 in decimal?

In a base 8 number system, what is the value of the number 57 in decimal?

Step 1: Identify the base of the number system. Here, the base is 8.
Step 2: Write down the number you want to convert, which is 57 in base 8.
Step 3: Break down the number 57 into its digits. The first digit is 5 and the second digit is 7.
Step 4: Determine the place value of each digit. The first digit (5) is in the '8s' place (8^1) and the second digit (7) is in the '1s' place (8^0).
Step 5: Calculate the value of the first digit: 5 * 8^1 = 5 * 8 = 40.
Step 6: Calculate the value of the second digit: 7 * 8^0 = 7 * 1 = 7.
Step 7: Add the values from Step 5 and Step 6 together: 40 + 7 = 47.
Step 8: The final result is that the base 8 number 57 is equal to 47 in decimal.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base 8 to decimal.
Exponentiation – Applying the correct powers of the base (8 in this case) to each digit based on its position.
Place Value – Recognizing the significance of each digit's position in a number system.