If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Multiplying & dividing in scientific notation

Learn how to simplify a multiplication and division expression using scientific notation. The expression in this problem is (7 * 10^5) / ((2 * 10^-2)(2.5 * 10^9)). 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 .
• 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!
• At , Sal says that his fraction can be viewed as 7/5 * 10^5/10^7. Is there any section or video where I can learn the things that fractions can do and how to work well with them?
• Search up 'Fractions' and choose the section you want to learn: for example, 'Multiplying and Dividing Fractions'.
• 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
• At to , I wish he would have wrote out the 10^5-10^7 to show what he did in his head.
• 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.
• Can you subtract exponents if the base is not the same?
• When dividing expressions that use exponents, we can subtract exponents only when the bases are the same.
• 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.
• Yes you are correct and you've made a good point. Great catch!