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### Course: 6th grade foundations (Eureka Math/EngageNY)>Unit 4

Lesson 2: Topic B: Foundations

# Dividing a decimal by a power of 10

Sal talks about why moving the decimal point to the left when dividing by a power of 10 makes sense. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• If I had 72.3 times 23.5 how would I do that
• I am not going to judge how easy multiplying decimals is easy or not, but I will show you an O.P strategy of solving these kind of problems.

When solving these questions you should ignore the decimal points and multiply it like a whole number.
Then the number of decimals spaces from the original spaces will go to the answer.
That sounded pretty hard, but it's not.
Lets solve your problem 72.3 × 23.5.
SO lets ignore the decimals and multiply 723 × 235.
You should get 169905.
Now in the original equation there were two numbers and each of them had one place to the left so we will make it two places to the left because of the two numbers.
You should have gotten 1699.0
• How many times do you need to divide 4379.9 by ten to get 4.3799?
• You need to divide 4379,9 by 1000 to get 4,3799. That would mean you will need to divide it by 10 three times (10^3 = 1000).

An easy trick to remember, is to count how many spaces you have to move the point to the left. Here, you have to move it to the left 3 times (from 4379.9 to 4.3799), so you have to divide it by 10 three times.
Likewise, to go from 4.3799 to 4379.9, you have to move the point 3 spaces, but to the right this time. This means that you have to multiply 4.3799 by 10 three times to get 4379.9.
• Does that mean if you do 0.001 divided by 100 I would just move the decimal right 2 times?
• Move the decimal place left two times. 0.001 divided by 100 = 0.00001. Place value goes up and down by powers of 10. Every time you multiply by 10, you go up a place value and every time you divide by 10, you go down a place value. When you divide 0.001 by 100, you’re basically dividing 0.001 by 10 twice, so you go down two place values.
• Please show a pattern that is easy to understand .. When multiplying a decimal by a power of ten
• Well, a pattern is:
0.001 * 10 = 0.01
0.001 * 100 = 0.1
0.001 * 1000 = 1
So, every time you multiply a number by ten you move the decimal place 1 place value to the right. And the same applies to numbers you usually don't see with decimal points, such as 1, 2, 3, etc.:
1*10 = ?(I know you probably already know this, but I'm providing an example)
Remember:
1.0 * 10 =
10.0
• why do you keep dividing the same number?
• Yea I don't know why he dose that
• why do we get a lower number
• Because when we divide, we change the whole number into groups of the whole number. For example, 4 divided by 2 means that only 2 groups of 2 will fit into 4, so 2 is the answer. Hope this helps! :D
• Do you always need to put a zero after the number after the decimal? For example, when your product for an answer is 3.20, do you have to keep that extra zero? Please reply A.S.A.P.
• No, 3.20 can just be written as 3.2. The zero on the end does not change the number.