If 'x' in base-7 is equal to 50 in decimal, what is 'x'?

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Question: If \'x\' in base-7 is equal to 50 in decimal, what is \'x\'?

Options:

Correct Answer: 110

Solution:

50 in decimal is \'110\' in base-7 (1*7^2 + 1*7^1 + 0*7^0 = 50).

If 'x' in base-7 is equal to 50 in decimal, what is 'x'?

If 'x' in base-7 is equal to 50 in decimal, what is 'x'?

Step 1: Understand that we need to convert the decimal number 50 into base-7.
Step 2: Find the largest power of 7 that fits into 50. The powers of 7 are 1 (7^0), 7 (7^1), 49 (7^2). The largest is 49 (7^2).
Step 3: Determine how many times 49 fits into 50. It fits 1 time. So, we write down 1 for the 7^2 place.
Step 4: Subtract 49 from 50. This gives us 1 (50 - 49 = 1).
Step 5: Now, we need to represent the remaining 1 in base-7. The next power of 7 is 7^1, which is 7. It fits 0 times into 1. So, we write down 0 for the 7^1 place.
Step 6: The remaining value is still 1, which is 1 in the 7^0 place. So, we write down 1 for the 7^0 place.
Step 7: Combine the digits we found: 1 (for 7^2), 0 (for 7^1), and 1 (for 7^0). This gives us '110' in base-7.

Base Conversion – Understanding how to convert numbers from decimal (base-10) to other bases, specifically base-7 in this case.
Place Value System – Recognizing the significance of each digit's position in a number when expressed in a specific base.