# Decimal-to-Octal Conversion

In the process of decimal-to-octal conversion progressive division in the case of the integer part and the progressive multiplication on the fractional part has been carried out by ‘8’ which is the radix of the octal number system. Again, the integer and fractional parts of the decimal number are treated separately.

e.g.

Find the octal equivalent of (73.75)10
Solution:
• The integer part = 73
Divisor                                             Dividend                                             Remainder
8                                                                 73                                                               —
8                                                                   9                                                                1
8                                                                   1                                                                1
—                                                                 0                                                                 1

• The octal equivalent of (73)10 = (111)8
• The fractional part = 0.75
• 0.75 × 8 = 0 with a carry of 6
• The octal equivalent of (0.75)10 = (.6)8
• Therefore, the octal equivalent of (73.75)10 = (111.6)8