Scientific notation

mathew281

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Jan 25, 2019
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2
Hi everyone,

would you please help me how did we get into this solution ?

< imgur URL removed -- see this notice >
 
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Subhotosh Khan

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Jun 18, 2007
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18,135
Hi everyone,

would you please help me how did we get into this solution ?
We do not visit that "imgur" for variety of reasons. You can write your work out in ASCII or post an image of your problem here.
 
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mathew281

New member
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Jan 25, 2019
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2
Screen Shot 2019-01-25 at 6.13.52 AM.png

this is my image, hope it's clear
 

Dr.Peterson

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Nov 12, 2017
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View attachment 10957

this is my image, hope it's clear
Please explain where you are confused; what result did you get?

They divided 1*10^-14 by 1.2*10^-4. So you have to divide 1 by 1.2, and 10^-14 by 10^-4, then make an adjustment. We'll want to see how far you got it correctly, so we can provide the help you need.
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
4,795
"\(\displaystyle 1\times 10^{-14}\)" is a decimal point, 13 "0"s, then a "1": 0.00000000000001.
"\(\displaystyle 1.2\times 10^{-4}\)" is a decimal point, 3 "0"s, then "12": 0.00012.

\(\displaystyle \frac{0.00000000000001}{0.00012}\). Hopefully, you learned to divide such thing by first moving the decimal point in both numerator and denominator to the right 5 times so the denominator is a whole number: \(\displaystyle \frac{0.000000001}{12}\). And to do that division, you first write all of those "0"s in the numerator then think "I can't divide 10 by 12 so I write another 0 and append a 0 to the numerator: 100/12. 12*8= 96 so 12 goes into 100 8 times with remainder 100- 96= 4. Append another 0. 12 divides into 40 3 times, 3*12= 36, with remainder 4. and now we continue getting "3"s. \(\displaystyle \frac{0.00000000000001}{0.00012}= 0.0000000000000083333...\). The "..." indicates that the "3"s keep repeating without end.

Very tedious.

A little simpler is to write \(\displaystyle \frac{1\times 10^{-14}}{1.2\times 10^{-4}}= \frac{1}{1.2}\frac{10^{-14}}{10^{-4}}= \frac{1}{1.2}\times 10^{-14-(-4)}= \frac{1}{1.2}\times 10^{-10}\) and then calculate that \(\displaystyle \frac{1}{1.2}= 0.83333...= 8.333...\times 10^{-1}\) so that \(\displaystyle \frac{1\times 10^{-14}}{1.2\times 10^{-4}}= 8.333...\times 10^{-11}\).
 
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