How do you convert 30.6 to octal number?

Answer 1

30.610 = 36.4631...8 (with the 4631 recurring).

I converted it by separating it into 30 + 0.6.

The 30 I converted by the usual method of dividing by the new base to get a quotient and remainder; then dividing the quotient by the base and repeating until the quotient is zero and the remainders in reverse order are the whole number in the new base.

The 0.6 I converted by seeing how many 1/8s are in 0.6, which gives the first digit after the octal point. Subtracting this, from 0.6 then left me with finding how many 1/82 = 1/64s are in the remainder to give the next digit after the octal point and so on. This I actually did by dividing 0.6 by 1/8 which is the same as multiplying it by 8 which gives a whole number (the next digit after the octal point) and a decimal part; I then repeated by multiplying the decimal part by 8 and so on:

30 ÷ 8 = 3 r 6

3 ÷ 8 = 0 r 3

⇒ 3010 = 368

0.6 x 8 = 4 + 0.8

0.8 x 8 = 6 + 0.4

0.4 x 8 = 3 + 0.2

0.2 x 8 = 1 + 0.6

at which point the digits repeat giving the answer as 30.610 = 36.4631...8