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# decimal 220.59 to octal?

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decimal 220.59 to octal?

Guest Aug 2, 2015

#1
+94140
+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 #1 +94140 +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
+92820
+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
+94140
+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