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### Course: Algebra basics>Unit 6

Lesson 4: Scientific notation intro

# Scientific notation example: 0.0000000003457

Can you imagine if you had to do calculations with very, very small numbers? How would you handle all those zeros to the right of the decimal? Thank goodness for scientific notation! Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• is there a concept for this?
• Chemistry and physics use large numbers and this format helps us deal with large and small numbers.
• Is there any short variant for writing 100000000000000000005000000000000000 in scientific notation?
• Counting Zeroes... clunk

100,000,000,000,000,000,005,000,000,000,000,000
Reporter:
Here lies 100 decillion 5 quadrillion in its natural habitat. How do we simplify this dinosaur? Like in word form, one could split the numbers apart, so in scientific notation, we could also split the numbers apart. Here we have 100 decillion 5 quadrillion with its liver a-chopped and innards askew.
`(1•10^35) + (5•10^15)`
Something of that sort, should be fine and dandy. Hope this helps! :-)
• Hi, I have a question, I was doing practice on Khan Academy site. There was a question 52 thousandths, which I have to turn in scientific notation, I answered 5.2x10^4 because I know 52000 has 3 zeros and I also add 2, so it gave me 10^4 but I was shocked it is incorrect, but why? Can anyone tell me?
• Well the answer will be 5.2*10^-2. Because you have written thousandths not thousands. Both are very different. thousands are on the left side of the decimals but thousandths will be on the right side of the decimal. By the was 52 thousandths will be 0.052
• Anyone wanna ride the struggle bus with me?
• its kinda making sense though.
(1 vote)
• what is the easiest way to solve scientific notation.
• Hi Epaintsil,
There isn’t really a ‘easier’ way, so I’ll try to explain as best as I can. So a random number with TONS of zeros, 62427000000, how can we possibly simplify this? I can’t just write that TERRIBLY long number forever!

So scientific notation is like: x * 10^y, where x is a number between 1 and 10, including the 1 and 10.

In our case, our number, n, can be changed onto 6.2427, because that’s the only way we can fit it into our 1-10.

So now we have x in our equation, what’s y?

How I find this, is I count the digits that are to the right of the decimal point, which is 4, plus the amount of 0s, which leads to 10 digits in total.

Y is 10, and X is 6.2427. Putting that into our equation ( x * 10^y, remember?), gives us 6.2427 * 10^10. And that’s the answer!

If you have any questions, or have figured a mistake, please reply. Otherwise, upvote and have a great day! (Not forcing you to upvote though :) )
• There is no end to the math
• me monkey brain this hurt head ooga ooga ;(
• can someone teach me how to do this I dont really understand (simplify what Sal said)
• basically it is a way of showing a really tiny number with a lot of zeros without writing 0.0000000ect
so if you have 0.000000000034 and you wanted to write it in scientific notation then you count the zeros and look at the numbers that aren't zeros and then take them and rewrite the problem as 3.4, then when you know how many zeros there are you do 3.4 * 1 to the -10 power
and if you were to solve that you would get the original number.
in short scientific notation is a way to simplify numbers.
Hope this helps!