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### Course: Class 7>Unit 5

Lesson 5: Large numbers in standard form

# Introduction to scientific notation

Introduction to scientific notation. An in-depth discussion about why and how scientific notation is used. Created by Sal Khan.

## Want to join the conversation?

• at Sal finishes a problem as 40x10^-7
could that be simplified to 4x10^-6 ?
• Yes. 40x10^-7 is the same as 4x10^-6
As a general rule, you would want to use the second option because in scientific notation, the number multiplied by the (10^n) should be between 1 and 10. 40 is not between 1 and 10, but 4 is.
For example, if I want to put 35,071 into scientific notation, I would put the decimal in between the 3 and the 5 like this: 3.5071 x 10^4.
• How did Avogadro's number get its name?
• The name "Avogadro's Number" is surely just an honorary name attached to the calculated value of the number of atoms, molecules, etc. in a gram molecular weight of any chemical substance. Of course if we used some other mass unit for the mole such as "pound mole", the "number" would be different. The first person to have calculated the number of molecules in any mass of substance seems to have been Josef Loschmidt, (1821-1895), an Austrian high school teacher, who in 1865, using the new Kinetic Molecular Theory (KMT) calculated the number of molecules in one cubic centimeter of gaseous substance under oridnary conditions of temperature of pressure, to be somewhere around 2.6 x 1019 molecules. This has always been known as the "Loschmidt Number."

I have been searched for some time to determine the first time the term "Avogadro Number" was used. My best estimate is that it was first used in a 1909 paper by Jean Baptiste Jean Perrin (1870-1942) entitled "Brownian Movement and Molecular Reality." This paper was translated into English from the French in "Annales De Chimie et de Physique" by Fredric Soddy and is available. Perrin, was the 1926 Nobel Laureate in Physics for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium. Perrin should be very well known to Dr. Northrup, of our chemistry department here at TTU who does calculation in molecular dynamics using methods developed by Perrin. In his paper Perrin says "The invariable number N is a universal constant, which may be appropriately designated "Avogadro's Constant."

In a simple minded way, here is how it might have come about:

First chemists discovered the combining ratios of the elements by mass. Those are the atomic weights. e.g. Na and Cl combine on a 1:1 ratio BY ATOM; BY MASS they combine on a 23 gram to 35.5 gram ratio. This has to mean that an atom of Na weighs less than an atom of Cl.
The Atomic Weight scale was worked out by observations like these.
Next chemists decided to take the Atomic Weight of an element and define that many grams of it to be ONE MOLE. That meant that 1 gram of H is a mole of H; 12 grams of C is a mole of C 23 grams of Na is a mole of Na, etc.
Finally they measured how many atoms are in ONE MOLE. It comes out to be the number 6.023x1023 atoms Therefore 1 mole of substance = 6.023x1023 particles. This is called Avogadro's Number. (credit to the friend that helped me with part of this)
• How do you show your real life example "30,000,000,000 cm/s" in scientific notation?
• 30,000,000,000 cm/s=3 x 10^10 cm/s
• I didn't know where to ask this and have reviewed this a long time ago but I'm coming back to it since I feel this is the best place to ask my question.

Sometimes when I'm just goofing off with a calculator and typing ENORMOUS numbers and multiplying them, then it says

9,999,999,999*9,999,999,999=1e+20 try it right now with google.

What does this,"e," mean and does it have ANYTHING to do with scientific notation?

Thanks for reading if you did. Vote up if you had the same question... People are forgetting what votes ARE but that's completely unrelated. Have a nice day!
• Indeed, e in that case represents the exponentiation of 10... which is the idea behind scientific notation!
Try taking the result you got on Google and divide it by 10. You should see the number after the e being decremented by 1.
• Thanks for all the help but
I am wondering how to do scientific notation with negative numbers?
• I hope I can help you out. Well, if you have this number...(^=exponent)
3.823200000^-9
you would have to count backwards to get the scientific notation.
• I know this is complicated but read the whole thing and you will understand hopefully.

I have 2 questions.

1.If you get something like googol,that in scientific notation would be
,,,,100
10

But how would you do it in scientific notation if it were a number like googol with a lot of 0's and an interruption in the middle like 100000000000...174 more 0's come by then 7 like 100000000.......70000000000000000000000000000000000...then 281 more 0's *How would you do that?*

2.Isn't googol(mentioned at ) x googol = googolplex,and is that in scientific notation
,,,,10,000
10
?
• 1. You would just put the number as 1.000000000007^100. The base doesn't have to be an integer.

2. A googolplex is a one with a googol zeros, NOT 10,000.
The real number in scientific notation would have been something like:

10^10^100 or 10^Googol
(1 vote)
• Hi I don't get scientific notation
• Turning into standard form

Positive Power
You have to multiply the number with your standard form of your exponent. As in the below given example the power is 7, so there should be seven zeros after 1.
1.432 * 10^7
= 1.432 * 10000000
= 14320000

Negative Power
You have to divide the number with your standard form of your exponent. As in the below given example the power is 7, so there should be seven zeros after 1.
1.432 * 10^-7
= 1.432/10000000
= 0.0001432
• Is there any tricks to scientific notation.
• Yes. Number is to try understanding exponents and then practice turning standard form numbers into scientific notation numbers.
(1 vote)
• Nice video, but lets not forget Mr. Krabs sold Spongebobs soul for 62 cents.
• What does "beat a dead horse" mean, Sal said it at ? I don't understand this metaphor.