In a certain numeral system, the number '23' represents 15 in decimal. What does

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Question: In a certain numeral system, the number \'23\' represents 15 in decimal. What does \'32\' represent?

Options:

Correct Answer: 22

Solution:

\'23\' in this system is 15. \'32\' would represent 22 in decimal.

In a certain numeral system, the number '23' represents 15 in decimal. What does '32' represent?

In a certain numeral system, the number '23' represents 15 in decimal. What does '32' represent?

Step 1: Understand that '23' in this numeral system equals 15 in decimal.
Step 2: Determine the base of the numeral system. Since '23' represents 15, we can express it as 2*base + 3 = 15.
Step 3: Solve for the base: 2*base + 3 = 15. Subtract 3 from both sides to get 2*base = 12.
Step 4: Divide both sides by 2 to find the base: base = 12 / 2 = 6.
Step 5: Now, convert '32' in this numeral system to decimal. '32' means 3*base + 2.
Step 6: Substitute the base value: 3*6 + 2 = 18 + 2 = 20.
Step 7: Therefore, '32' represents 20 in decimal.

Base Conversion – Understanding how to convert numbers from one numeral system to another, particularly when the base is not immediately clear.
Place Value – Recognizing the significance of the position of digits in a numeral system and how it affects the overall value.