# Octal fractions to decimal numbers

This post is explain

Example 1:

Convert Octal number 0.725 to decimal number

Completion:

0.725

1st digit after octal point: 7 → 7 × (1/ 8

2nd digit after octal point: 2 → 2 × (1/ 8

3rd digit after octal point: 5 → 5 × (1/ 8

sum all → 0.875 + 0.03125 + 0.009765625 = 0.916015625

0.725

Example 2:

Convert octal number 105.2063 to decimal number

Completion:

105.2063

1st digit: 5 → 5 × 8

2nd digit: 0 → 0 × 8

3rd digit: 1 → 1 × 8

sum all → 5 + 0 + 64 = 69

1st digit: 2 → 2 × (1/ 8

2nd digit: 0 → 0 × (1/ 8

3rd digit: 6 → 6 × (1/ 8

4th digit: 3 → 3 × (1/ 8

sum all → 0.25 + 0 + 0.01171875 + 0.000732423 = 0.262451173

501.2063

**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 |

Convert Octal number 0.725 to decimal number

Completion:

0.725

_{(8)}= ...

_{(10)}

1st digit after octal point: 7 → 7 × (1/ 8

^{1}) = 7 × 0.125 = 0.875

2nd digit after octal point: 2 → 2 × (1/ 8

^{2}) = 2 × 0.015625 = 0.03125

3rd digit after octal point: 5 → 5 × (1/ 8

^{3}) = 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 × 8

^{0}= 5 × 1 = 5

2nd digit: 0 → 0 × 8

^{1}= 0 × 8 = 0

3rd digit: 1 → 1 × 8

^{2}= 1 × 64 = 64

sum all → 5 + 0 + 64 = 69

*after octal point*

1st digit: 2 → 2 × (1/ 8

^{1}) = 2 × 0.125 = 0.25

2nd digit: 0 → 0 × (1/ 8

^{2}) = 0 × 0.015625 = 0

3rd digit: 6 → 6 × (1/ 8

^{3}) = 6 × 0.001953125 = 0.01171875

4th digit: 3 → 3 × (1/ 8

^{4}) = 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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