# Scientific notation

#### mathew281

##### New member
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

##### Super Moderator
Staff member
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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#### Dr.Peterson

##### Elite Member
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
"$$\displaystyle 1\times 10^{-14}$$" 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 $$\displaystyle \frac{1\times 10^{-14}}{1.2\times 10^{-4}}= 8.333...\times 10^{-11}$$.