Question

Convert 13754_8 to base 10.

Answer 1

The number 137548 is equal to 6124 in base 10.

Step-by-step explanation:

To convert the number 137548 to base 10, we need to multiply each digit of the number by the corresponding power of 8 and then sum up the results.

Starting from the rightmost digit, we have:

• The digit 4 multiplied by 80 (which is 1) equals 4.
• The digit 5 multiplied by 81 (which is 8) equals 40.
• The digit 7 multiplied by 82 (which is 64) equals 448.
• The digit 3 multiplied by 83 (which is 512) equals 1536.
• The digit 1 multiplied by 84 (which is 4096) equals 4096.

Now, we sum up the results: 4 + 40 + 448 + 1536 + 4096 = 6124.

Therefore, 137548 is equal to 6124 in base 10.

Answer 2

To convert a number from base 8 (octal) to base 10 (decimal), you can use the positional notation. Each digit in the octal number represents a power of 8. Here's how you can convert 13754₈ to base 10:

1 × 8^4 + 3 × 8^3 + 7 × 8^2 + 5 × 8^1 + 4 × 8^0

= 4096 + 1536 + 448 + 40 + 4

= 6134

Therefore, the octal number 13754₈ is equivalent to the decimal number 6134.

Step-by-step explanation: