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# 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
• Is there any application for scientific notation?
• Yes, there is! When dealing with big and long numbers, it can really be a pain writing out all of them, this is when scientific notation helps out! For example it will be really hard to write 300000000000, so we write it like 3•10^11
• Is there anywhere in the real world that we would use scientific notation other then a math worksheet?
• Sure... many sciences deal with very large and very small numbers. Some examples would be: distances between planets or solar systems, the size of small things like atoms, etc. These numbers may have too many digits for calculators to display. Scientific notation is needed in those situations. And, calculators will sometimes give results in scientific notation when you input a calculation that results in a number to large to display.
• Is there an algorithm for this?
• Technically what Nathan said is true, what the video explained has an "algorithm" to find "this'. Nathan just restated... etc
• how do you convert an ending equation like 3.05 x 10^5 back to scientific notation though?
Do you mean how do you go back to standard notation? If yes, you just need to shift the decimal point. The 10^5 means you are multiplying by 5 instances of 10. Each 10 shifts the decimal point 1 place to the right (you get a bigger number). Since there are 5 10's, shift the decimal point 5 places to the right and you get 305000 or 305,000

If the exponent had been negative 5, then you are essentially dividing by 5 tens and the decimal point will shift left (creating a smaller number).

Hope this helps.
• Does it always have to be a decimal or can it be like 32 * 10^2 instead of 3.2 * 10^3?
• The number can never exceed 10, so it would be wrong to use 32 instead of 3.2. That being said, you can still have it as whole numbers that are less than ten. For example, 300 would turn into 3 * 10^2.