# Octal fractions to decimal numbers

This post is explain how to convert octal fractions to decimal numbers. The picture below is show octal fraction to decimal, form 1st position to 5th position of the digit, before and after the octal point.
 Octal fractions to decimal
Example 1:
Convert Octal number 0.725 to decimal number

Completion:
0.725 (8) = ... (10)
1st digit after octal point: 7 → 7 × (1/ 81) = 7 × 0.125 = 0.875
2nd digit after octal point: 2 → 2 × (1/ 82) = 2 × 0.015625 = 0.03125
3rd digit after octal point: 5 → 5 × (1/ 83) = 5 × 0.001953125 = 0.009765625
sum all → 0.875 + 0.03125 + 0.009765625 = 0.916015625

0.725 (8) = 0.916015625 (10)

Example 2:
Convert octal number 105.2063 to decimal number

Completion:
105.2063 (8) = ... (10)

before octal point
1st digit: 5 → 5 × 80 = 5 × 1 = 5
2nd digit: 0 → 0 × 81 = 0 × 8 = 0
3rd digit: 1 → 1 × 82 = 1 × 64 = 64
sum all → 5 + 0 + 64 = 69

after octal point
1st digit: 2 → 2 × (1/ 81) = 2 × 0.125 = 0.25
2nd digit: 0 → 0 × (1/ 82) = 0 × 0.015625 = 0
3rd digit: 6 → 6 × (1/ 83) = 6 × 0.001953125 = 0.01171875
4th digit: 3 → 3 × (1/ 84) = 3 × 0.000244141 = 0.000732423
sum all → 0.25 + 0 + 0.01171875 + 0.000732423 = 0.262451173

501.2063 (8) = 69.262451173 (10)
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