Final answer:
To convert from decimal to octal, divide the number by 8 and write down the remainders. For 456, the octal is 710. For 117.16, the whole number part is 165 and the fractional part is approximately .12 in octal.
Step-by-step explanation:
To convert from decimal to octal, you divide the decimal number by 8 and write down the remainder. Continue dividing the quotient by 8 and writing down the remainders until the quotient is 0. The octal number is then the remainders read in reverse (from last to first).
Example:
456 in decimal to octal:
456 ÷ 8 = 57 remainder 0
57 ÷ 8 = 7 remainder 1
7 ÷ 8 = 0 remainder 7
Reading the remainders backwards, we get 710 in octal.
117.16 in decimal to octal:
117 ÷ 8 = 14 remainder 5
14 ÷ 8 = 1 remainder 6
1 ÷ 8 = 0 remainder 1
So, the whole number part is 165 in octal. To convert the decimal part (0.16), we need to multiply it by 8 and take the integer part of the result, repeatedly:
0.16 × 8 = 1.28 (integer part is 1)
0.28 × 8 = 2.24 (integer part is 2)
You can continue this process to get more digits of precision. For now, the octal representation is approximately 165.12