Question

Convert from decimal to octal:
a. 456
b. 117.16

Answer 1

To convert decimal to octal, divide the number by 8, take the remainder as the next digit, and continue with the quotient. For 456, the process yields the octal number 710. For the decimal number 117.16, convert the whole and fractional parts separately to get approximately 165.12 in octal.

Step-by-step explanation:

To convert a number from decimal to octal, you divide the number by 8 and write down the remainder. Continue to divide the result by 8 until you get to 0, and write down the remainders in reverse order. Let's see how this works for the numbers 456 and 117.16.

Convert 456 from decimal to octal

1. 456 ÷ 8 = 57 with a remainder of 0.
2. 57 ÷ 8 = 7 with a remainder of 1.
3. 7 ÷ 8 = 0 with a remainder of 7.

Write down the remainders in reverse order to get the octal number 710.

Convert 117.16 from decimal to octal

To convert the fractional part, multiply by 8 and take the whole number part as the result. Continue multiplying the fractional part by 8 and taking the whole number until the fractional part becomes 0 or until you have enough digits.

1. For the whole number part 117, use the method above to get 165 in octal.
2. Multiply the fractional part 0.16 by 8 to get 1.28, the whole number 1 is the first digit after the decimal point in octal.
3. Take the fractional part .28 and multiply by 8 to get 2.24, the whole number 2 is the second digit.
4. Repeat this process until the desired precision is reached.

Let's stop at two digits for simplicity. The octal number for 117.16 is approximately 165.12 in octal.