+0

decimal 220.59 to octal?

0
298
3

decimal 220.59 to octal?

Guest Aug 2, 2015

Best Answer

#1
+91435
+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 Sort: 3+0 Answers #1 +91435 +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
+80935
+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
+91435
+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

4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details