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### Course: Math (NSDC) - English>Unit 7

Lesson 5: Arithmetic with numbers in scientific notation

# Multiplying & dividing in scientific notation

In order to simplify multiplication and division using scientific notation, you should multiply and divide numbers with the same base, and add or subtract the exponents. Through this process, complex expressions can be simplified into a single value multiplied with 10 to a certain power. As an example, 7 times 10 to the fifth over 2 times 10 to the negative 2 times 2.5 times 10 to the ninth can be simplified to 1.4 times 10 to the negative 2. Scientific notation helps to simplify complex equations that involve multiplying and dividing numbers with the same base. Created by Sal Khan.

## Want to join the conversation?

• I need help how did you get 5 from 2 x 2.5 on my calculator i got 4.5
• my friend, you put a + instead of a x... 2 + 2.5 = 4.5 --- 2 x 2.5 = 5 .
• Does the first factor in the answer need to have a decimal point in it always? Or are there exceptions for problems where if you simplify them another way, the first digit ends up being zero? My question isn't specific to this video, just a general question on this topic.
• The format for scientific notation is that there will always be just 1 digit to the left of the decimal point and that digit can not be zero.
For example:
9,300,000 becomes 9.3 x 10^6
0.0005 becomes 5 x 10^(-4)
Hope this helps.
• When I first saw this, I thought, Oh shoot!, but after I watched the whole video through, I realised that it's actually quite easy! So if anyone is struggling with it, trust me, you'll get it eventually.
• I get the multiplication, but the division looks like common core. 😳😔😫😡
• i hate math bruh
• bro y so hard
• Is there a reason why one puts the point right after the first significant figure when using scientific notation? E.g. 245324.321 as 2.45324321*10^5 instead of 245.324321*10^3? I think the last notation is smarter because it is easier to see that the number is a thousand-something.
• In scientific notation, the number has to be from 1 - 9. For example, 3.1415926 x 10^7 is correct instead of 31.415926 x 10^6 which is incorrect.
I know this is a late response, but I hope this helped anyone!
• What do I do if the product/quotient is not appropriate for scientific notation? For example (5.0 x 10^1) x (2.0 x 10^1) which I imagine equals 10 x 10^2. If I had to guess I'd say increase 10^2 to 10^3 and make 10 to 1.0 so that it'd be 1.0 x 10^3. Sorry for any poor wording
• Did Sal make an error here? At , he is checking to see if 1.4 * 10^-2 is expressed in scientific notation. After confirming that 1.4 is greater than or equal to one, he next asks if it is less than or equal to nine.

But the rule for scientific notation is that the decimal portion of the number must be less than (and not equal to ) 10. If I wrote a number like 9.9 * 10^-2, this would be a decimal that is not less than or equal to nine, but it would be in scientific notation, because the rule is that the decimal must be greater than or equal to one and less than 10.