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The decimal equivalent of an octal number 234.32 is ?

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jora7 | Student, Undergraduate | (Level 1) Honors

Posted February 23, 2012 at 1:33 PM via web

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The decimal equivalent of an octal number 234.32 is ?

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted February 23, 2012 at 1:54 PM (Answer #1)

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Octal number means number in base 8, to convert it back to decimal(or base 10) we will multiply by powers of 8. `2*8^2+3*8+4*8^0+3*8^(-1)+2*8^(-2)=` `3076.40625` Answer is 3076.40625
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Matthew Fonda | eNotes Employee

Posted February 24, 2012 at 3:18 AM (Answer #2)

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Our goal is to write 234.32 octal (base 8) in decimal. In octal, instead of having a ones place, tens places, hundreds place, etc. like you do in decimal, you have a 1's place, 8's place, 64's place, etc. Notice that these are just powers of 8.

So to write 234.32 in decimal, we have:

`2*8^2 = 128`

`3*8^1 = 24`

`4*8^0 = 4`

.

`3 * 8^-1 = 0.375`

`2 * 8^-2 = 0.03125`

We add these all up (128+24+4+0.375+0.03125), giving us our answer, 156.40625

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