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decimal 220.59 to octal?

Guest Aug 2, 2015

Best Answer 

 #1
avatar+91001 
+10

change   220.59 base 10 to base 8

 

Mmm, the whole number part is easy enough

220/8 = 27 remainder 4

27/8=3 remainder 3

3/8=0 remainder 3

so     $$220_{10}=334_8$$

 

Now the decimal part - I have never done this before.

There is no power of 8 that is also a power of 10 so it will have to be an approximation.

I will work it out to 3 base 8  places and then round it back to 2 I think.

$$\\\frac{59}{10^2}=\frac{x}{8^3}\\\\
59*8^3/100 = 302.08\\\\
so\;\;\;\; X\approx 302\\\\
\frac{59}{10^2}\approx \frac{302}{8^3}\\\\
$now change $302_{10}$ to base 8$\\\\$$

302/8=37 remainder 6

37/8=4 remainder 5

4/8= 0 remainder 4

so

$$\\302_{10}=456_{8}\\\\
so\\\\
0.59 \;(base10)\approx 0.456\; (Base8) \approx 0.46 \;\;$to 2 base 8 places$$$

 

SO 

 

$$220.59_{10}\approx 334.46_{8}$$

 

I just checked it with Wolfram alpha and it is correct  

http://www.wolframalpha.com/input/?i=change+220.59+to+base+8

Melody  Aug 2, 2015
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3+0 Answers

 #1
avatar+91001 
+10
Best Answer

change   220.59 base 10 to base 8

 

Mmm, the whole number part is easy enough

220/8 = 27 remainder 4

27/8=3 remainder 3

3/8=0 remainder 3

so     $$220_{10}=334_8$$

 

Now the decimal part - I have never done this before.

There is no power of 8 that is also a power of 10 so it will have to be an approximation.

I will work it out to 3 base 8  places and then round it back to 2 I think.

$$\\\frac{59}{10^2}=\frac{x}{8^3}\\\\
59*8^3/100 = 302.08\\\\
so\;\;\;\; X\approx 302\\\\
\frac{59}{10^2}\approx \frac{302}{8^3}\\\\
$now change $302_{10}$ to base 8$\\\\$$

302/8=37 remainder 6

37/8=4 remainder 5

4/8= 0 remainder 4

so

$$\\302_{10}=456_{8}\\\\
so\\\\
0.59 \;(base10)\approx 0.456\; (Base8) \approx 0.46 \;\;$to 2 base 8 places$$$

 

SO 

 

$$220.59_{10}\approx 334.46_{8}$$

 

I just checked it with Wolfram alpha and it is correct  

http://www.wolframalpha.com/input/?i=change+220.59+to+base+8

Melody  Aug 2, 2015
 #2
avatar+78618 
+5

Very nice , Melody.....

 

I'm having trouble wrapping my head around this part.....

 

59 / 102   =  x / 83

 

How did you know to do this???

 

 

CPhill  Aug 2, 2015
 #3
avatar+91001 
+5

Thanks Chris :))

 

When working in base ten, the first place after the decimal point is  tenths, the second is tenths squared,  the third is tenths ^3  etc

 

When working in base eight, the first place after the decimal point is  eigths, the second is eigths squared,  the third is eigths ^3  etc

 

So I needed to change 59/10^2   to something over eight to the power of some positive integer.

I just chose to do it to three decimal places so I used 8^3.

 

Does that make sense?

Melody  Aug 3, 2015

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