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.

Lesson 4: Multiplying and dividing with powers of 10

# Exponents and powers of 10 patterns

This lesson explains calculations involving powers of ten. It demonstrates how to multiply and divide by these powers, and explains the results of these calculations, such as adding or removing zeroes from the end of a number. Additionally, the lesson discusses how these calculations can shift the placement of a decimal point to the left or right. Created by Sal Khan.

## Want to join the conversation?

• how do i know where i move the decimal
• Hello!
Let me try to answer this a little better for you...
When you're working with powers of ten and decimals, it's just a matter of remembering the system. To use Dania's example, let's say you had 92.84. Say you wanted to multiply it by 10^2. The decimal moves the same number of places to the right as the value of the exponent. So in this case, it is ten to the power of 2. Since it is a power of 2, you will move 2 places to the right, giving you 9284. If it were a higher power, say 10^5, you would move the decimal 5 places to the right. So if our equation is 92.84*10^5, you would move the decimal over 5 places to the right. If there aren't values in those places, just add zeroes. In this case it would be 9,284,000.
Hope this helps! Remember, this only works with positive powers of ten. Let me know if I can help more.
-Kendall
• WHat is 3^5 divided by 10^7=?
• 3^5=243
10^7=10000000
243/10000000=0.0000243
(1 vote)
• at of the video, Is that the easiest way we can do this?
• there's just two ways:
1x10x10x10x10x10;
10^5 add number of zeroes of the exponents 1 and five 0s(100000)
(1 vote)
• The power of 5 with ten is 100,000
• You are correct, good sir. Good to see you are applying your new knowledge. And I think you mean ten to the fifth power.
• what place does the power of 10 pattern move to , right or left ?
• the pattern moves to the right. And so that is how he is saying it.
• What will you get by 10 to power of 10?
10 x 10 to power of 10.
• you would get 10,000,000,000. Which is 10 billion i think
• if you divide 10^3 by 10^2 what would it be?
• `10^3/10^2 = 10`. Here are `2` ways you can approach this in your head:
1) Converting them into numbers, knowing powers of `10`:
`10^3/10^2 = 1000/100 = 10`
2) Expanding out the exponents, then cancelling:
`10^3/10^2 = (10*10*10)/(10*10) = 10/1 = 10`

I hope you got something from this! :]
(1 vote)
• so what about 1x10x10x10x10x10x10? it would be 6 x 100,000,000 wouldn't it? i'm confused
(1 vote)
• 10x10x10x10x10x10 is 10^6, or 10⁶. You count up the number of tens and use that as the exponent, and since ten is the thing being multiplied, that is the base.