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In a base-5 number system, what is the decimal equivalent of the base-5 number 2

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Question: In a base-5 number system, what is the decimal equivalent of the base-5 number 243?

Options:

  1. 35
  2. 60
  3. 55
  4. 50

Correct Answer: 35

Solution: 

To convert from base-5 to decimal, multiply each digit by 5 raised to the power of its position (from right to left, starting at 0). Thus, 2*5^2 + 4*5^1 + 3*5^0 = 2*25 + 4*5 + 3*1 = 50 + 20 + 3 = 73.

In a base-5 number system, what is the decimal equivalent of the base-5 number 2

Practice Questions

Q1
In a base-5 number system, what is the decimal equivalent of the base-5 number 243?
  1. 35
  2. 60
  3. 55
  4. 50

Questions & Step-by-Step Solutions

In a base-5 number system, what is the decimal equivalent of the base-5 number 243?
  • Step 1: Identify the base-5 number you want to convert, which is 243.
  • Step 2: Write down the digits of the base-5 number from right to left: 3 (5^0), 4 (5^1), and 2 (5^2).
  • Step 3: Multiply each digit by 5 raised to the power of its position: 2 * 5^2, 4 * 5^1, and 3 * 5^0.
  • Step 4: Calculate each multiplication: 2 * 5^2 = 2 * 25 = 50, 4 * 5^1 = 4 * 5 = 20, and 3 * 5^0 = 3 * 1 = 3.
  • Step 5: Add all the results together: 50 + 20 + 3 = 73.
  • Step 6: The decimal equivalent of the base-5 number 243 is 73.
  • Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-5 to decimal.
  • Positional Value – Recognizing the significance of each digit's position in a number system and how it affects the overall value.
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