How do you convert 225.25 to octal number?

Answer 1

To convert the whole part to another base:

1) divide the number by the new base to get a whole quotient and a remainder

2) note the remainder

3) replace the number by the quotient

4) if the number is not zero repeat from step 1

5) write the remainders in reverse order to get the number in the new base

To convert the fractional part to another base:

1) multiple the fractional part by the new base

2) note the whole number part

3) remove the whole number part to leave the fractional part

4) if the fractional part is not zero and the required accuracy has not been reached repeat from step 1

5) the noted whole parts in order are the fractional part in the new base.

The required accuracy condition is there in case the fractional part becomes repeating, eg 0.1 decimal in binary is repeating: 0.1 = 0.000110011001100... (repeating 1100) in binary.

For 225.25 to octal (base 8):

Whole part (225):

225 ÷ 8 = 28 r 1

28 ÷ 8 = 3 r 4

3 ÷ 8 = 0 r 3

→ 225 is 341 in octal

For the fractional part (.25):

0.25 x 8 = 2.0 → 2 and 0.0, so finish.

→ 225.25 in octal is 341.2