In a certain base, the number 'A3' represents 163 in decimal. What is the base o

₹0.0

Question: In a certain base, the number \'A3\' represents 163 in decimal. What is the base of this number system?

Options:

Correct Answer: 12

Solution:

Let the base be \'b\'. Then, A3 = 10*b + 3 = 163. Solving gives b = 12.

In a certain base, the number 'A3' represents 163 in decimal. What is the base of this number system?

In a certain base, the number 'A3' represents 163 in decimal. What is the base of this number system?

Step 1: Understand that 'A3' means A times the base plus 3. We need to find the base, which we will call 'b'.
Step 2: Recognize that 'A' in base 'b' represents 10 in decimal. So, we can write 'A3' as 10*b + 3.
Step 3: Set up the equation: 10*b + 3 = 163.
Step 4: Subtract 3 from both sides of the equation: 10*b = 163 - 3.
Step 5: Calculate the right side: 10*b = 160.
Step 6: Divide both sides by 10 to solve for 'b': b = 160 / 10.
Step 7: Calculate the division: b = 16.
Step 8: Realize that 'A' represents 10 in base 12, so we need to check if 'A3' in base 12 equals 163 in decimal.
Step 9: Confirm that 10*12 + 3 = 120 + 3 = 163, which is correct.

Base Conversion – Understanding how to convert numbers from a non-decimal base to decimal by using the positional value of each digit.
Algebraic Manipulation – Solving equations to find the unknown base by setting up an equation based on the value of the number in decimal.