Question

Convert 97 base 10 to base 5 (show steps).
convert 1234 base 8 to base 10 (show steps)

Answer 1

To convert 97 base 10 to base 5, divide 97 by 5 repeatedly and write down the remainders. The base 5 representation of 97 is 342. To convert 1234 base 8 to base 10, multiply each digit by the corresponding power of 8 and sum the results. The base 10 representation of 1234 base 8 is 668.

Step-by-step explanation:

To convert 97 base 10 to base 5, we divide 97 by 5 repeatedly and write down the remainders. The remainders, read backwards, give us the base 5 representation of 97. Here are the steps:

1. Divide 97 by 5: quotient = 19 and remainder = 2
2. Divide 19 by 5: quotient = 3 and remainder = 4
3. Divide 3 by 5: quotient = 0 and remainder = 3
4. Combine the remainders in reverse order: the base 5 representation of 97 is 342

To convert 1234 base 8 to base 10, we multiply each digit by the corresponding power of 8 and then sum the results. Here are the steps:

1. Multiply the first digit (1) by 8^3 (512): 1 * 512 = 512
2. Multiply the second digit (2) by 8^2 (64): 2 * 64 = 128
3. Multiply the third digit (3) by 8^1 (8): 3 * 8 = 24
4. Multiply the fourth digit (4) by 8^0 (1): 4 * 1 = 4
5. Sum up the results: 512 + 128 + 24 + 4 = 668