If 'A' in base-7 is equal to 50 in decimal, what is the value of 'A'?

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Question: If \'A\' in base-7 is equal to 50 in decimal, what is the value of \'A\'?

Options:

Correct Answer: 70

Solution:

In base-7, \'A\' = 5*7^1 + 0*7^0 = 35 + 0 = 50 in decimal.

If 'A' in base-7 is equal to 50 in decimal, what is the value of 'A'?

If 'A' in base-7 is equal to 50 in decimal, what is the value of 'A'?

Step 1: Understand that 'A' is a number in base-7.
Step 2: Recognize that in base-7, each digit represents a power of 7.
Step 3: Identify the digits in 'A'. Here, 'A' has two digits: 5 and 0.
Step 4: The first digit (5) is in the 7^1 place, and the second digit (0) is in the 7^0 place.
Step 5: Calculate the value of the first digit: 5 * 7^1 = 5 * 7 = 35.
Step 6: Calculate the value of the second digit: 0 * 7^0 = 0 * 1 = 0.
Step 7: Add the values from Step 5 and Step 6: 35 + 0 = 50.
Step 8: Conclude that 'A' in base-7 is equal to 50 in decimal.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-7 to decimal.
Positional Notation – Recognizing the significance of each digit's position in a number system, where each position represents a power of the base.