Convert octal fraction to decimal fraction

Solved examples of octal fractions to decimal fraction conversion

Problem 1: Convert ( 2 1 . 2 1 )₈= ( ? )₁₀

_{= 2 1 . 2 1}
↑ ↑
MSD LSD

= 2 x 8¹ + 1 x 8⁰ . 2 x 8^-1 + 1 x 8^-2

= 2 x 8 + 1 x 1 . 2 x ( 1 / 8 ) + 1 x ( 1 / 64 )

= 16 + 1 . ( 0. 2 5 ) + ( 0 . 0 1 5 6 2 5 )

= 17 + 0. 265625

= 17 . 265625

Therefore ( 2 1 . 2 1 )₈ = ( 1 7 . 2 6 5 6 2 5 )₁₀

Problem 2: Convert ( 0.357 )₈= ( ? )₁₀

_{= 0 . 3 5 7}
↑ ↑
MSD LSD

= 0 x 8⁰ . 3 x 8^-1 + 5 x 8^-2 + 7 x 8^-3

= 0 x 1 . 3 x ( 1 / 8 ) + 5 x ( 1 / 64 ) + 7 x ( 1 / 512 )

= 0 . (0. 375) + (0 . 0 7 8 1 2 5 ) + ( 0.013671875 )

= 0 . ( 0 . 466796875 )

= 0 . 466796875

Therefore ( 0 . 3 5 7)₈ = ( 0 . 466796875 )₁₀

Problem 3: Convert ( 100.01 )₈= ( ? )₁₀

_{= 1 0 0 . 0 1}
↑ ↑

MSD LSD

= 1 x 8²+ 0 x 8¹+ 0 x 8⁰ . 0 x 8^-1+ 1 x 8^-2

= 1 x 64+ 0 x 8+ 0 x 1 . 0 x ( 1 / 8 )+ 1 x ( 1 / 64 )


= 64 + 0 + 0  . ( 0 )+ ( 0. 015625 )

= 64  . ( 0. 015625 )

= 64 . 015625

Therefore ( 1 0 0 . 0 1 )₈ = ( 64 . 0 1 5 6 2 5 )₁₀

Octal to binary conversion procedure