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### Course: Arithmetic > Unit 17

Lesson 4: Multiplying and dividing with powers of 10# Fractions as division by power of 10

Explore the concept of multiplying and dividing numbers by powers of 10. Understand how moving the decimal point to the left or right changes the value of a number, and how this relates to the concept of fractions as division. Created by Sal Khan.

## Want to join the conversation?

- Would it be the sames if was 10/34?(11 votes)
- No, if it was 10/34, it would not be the same. That is because the numerator and denominator are not the same now. The answer (I got it from a calculator) is :

0.29411764705882352941176470588235(12 votes)

- i actully really dont get it hot did he make 34/10 into 3.4(4 votes)
- Dividing by 10 is the same as moving the decimal point one place to the left.

Note that 34 has a hidden decimal point just to the right of the digit 4.

So 34/10 = 3.4

Have a blessed, wonderful day!(15 votes)

- So is this just dividing the two numbers to get the answer? At8:34am. Please respond, people.(7 votes)
- No.You move the decimal over one spot for 10 ,two spots for 100 and so on.(4 votes)

- whats the difference of 0.1 and -1(5 votes)
- 0.1 and -1 have a difference of 1.1

0.1 is one tenth ABOVE zero while -1 is a whole one BELOW zero.(7 votes)

- so dividing to the power of ten is like dividing 1/the power of nine is like 1/ 90(6 votes)
- 1:51-1:53Might I ask why is it dangerous? I know it looks puzzling, but is that the only reason?(4 votes)
- It's dangerous because people don't know what's be4 the 7.(2 votes)

- for some reason this one was A LOT harder than it should've been..(4 votes)
- hello from the other side(1 vote)

- can a decimal have a decimal eg. 4.5.3? can that happen??(2 votes)
- I'm not whiz whatsoever but if I had to say, it would be no. A decimal denotes a fraction of a whole number. There is no such thing as a fraction of a fraction of a whole number.

The 1s place will always be there regardless of whether or not it's a 0 or another number.

4.5.3 is the same as saying 4 Ones, 5 Tenths, 3 Hundredths. The 2nd decimal doesn't contribute to the fraction in any way and shouldn't be placed there. In computer applications, version numbers are displayed with multiple decimals though.

in 4.5.3, 4 would mean the version number. 5 would mean small revisions done to version 4, and 3 would mean even smaller updates done to 4.5. So it would look something like Version 4 r5.3.(4 votes)

- why when you are multiplying you have to move it to the right but when you are dividing it goes to the left(3 votes)
- When you move the decimal point to the right by
`1`

, the number gets larger by being multiplied by`10`

.

Eg.`2.56*10`

:`2.56 -> 25.6`

which made the number`10`

x bigger.

When you move the decimal point to the left by`1`

, the number gets smaller by being divided by`10`

.

Eg.`25.6/10`

:`25.6 -> 2.56`

which made the number`10`

x smaller.(1 vote)

- If you divide a negitive number you get a bigger number. What happens if you divide -5 by 10? Does it turn positive? or is it -.5?(2 votes)
- If you multiply or divide a negative number by a positive number, the result will be negative.(3 votes)

## Video transcript

So I have six different
fractions written out here, and what I want you to do is
pause this video right now and try to rewrite each of
these fractions as a decimal. So I'm assuming you've
given a go at it, so let's go through
each of these. So we know that when we
say 34/10, or 34 over 10, that this could be interpreted
literally as 34 divided by 10. And so if you
start with 34-- let me put a little decimal
right over here. It will be clear that there
is an implied decimal there, so we could just keep
adding zeroes if we want. So when we divide
by 10, we're going to move the decimal one
space over to the left. And you should always
do a reality check. If you forget, hey, do I
move it over to the left, or do I do it over to the right? You should do a reality check. Look, if I'm dividing
by 10, should I get a smaller value
or a larger value? Well, clearly, if you're
dividing it into 10 groups, you should get a smaller value. So when you take your
decimal place to the left, you're going to get
a smaller value. 34 is going to become 3.4. And that makes complete sense. If you were to
multiply 3.4 by 10, you would move the
decimal to the right, and you would get to 34. Let's think about this one. So this one right
over here is 3.4. Now let's think about 7/10. So the exact same idea. This is equal to
7 divided by 10. This fraction, horizontal
line symbol thing could literally be
viewed as "divided by." This could be read
as 7 divided by 10. So when you divide by 10, you
move the decimal one space over to the left. So we're going to
get to point 7. And just to be clear, we
could write this as 0.7. It's sometimes dangerous
to just write the decimal without the zero out front. So 7/10, or 7 divided by
10, can be rewritten as 0.7. Now let's try 53/100. Well, we'll start with our 53. Once again, this
could be interpreted as 53 divided by 100. So there's an implied decimal
point right over here. Now, if we're dividing by
100, that's dividing by 10 and then dividing by 10 again. This is dividing by 10 times 10. So we're going to divide
by 10, and then we're going to divide by 100. So the decimal is going
to land right over there. So that's going
to get us to 0.53. Now let's tackle
2 divided by 100. So once again, this could be
rewritten as 2 divided by 100. 2/100 is the same thing
as 2 divided by 100. If we start with a 2, put our
decimal point right there. So we're going to
divide by 10, and we're going to do that twice. So we're going to
divide by 10 once. That would be 2/10. That puts our decimal there. But we have to
divide by 10 again. You might say, hey, look,
there's nothing here. Well, you could just
throw a zero on here, just so that you
do something there, and then you have moved your
decimal over to the left twice. Remember, every time
you're doing it, you're dividing by 10. You're dividing by 10. Then you're dividing
by 10 again. Dividing by 10 two times, that's
the same thing as dividing by 100, because 10
times 10 is 100. So this is going to be 0.02. Now we've already seen that, if
you were to try to read this, this 2 is in the
hundredths place. So you would literally
read this as 2 hundredths. And we see that right over here. We've literally represented
it as 2 hundredths right over there-- 2/100. So now we have 1,098
divided by 100. Well, same drill. Or 1,098 hundredths I could say. That's the same thing
as 1,098 divided by 100. So we could start with 1,098. The decimal is implicitly
right over here, but we need to move it two
spaces to the left-- one, two-- because we're dividing by 100. That gets us to 10.98. And always do a reality check. Look, it makes sense. We got to a significantly
smaller value when we divided by 100. Now we'll just divide
9,967 by 1,000. Well, 9.967, decimal
point implicitly there. Now, 1,000 is 10
times 10 times 10. So if you're dividing
by 1,000, that's dividing by 10 three times. So we'll divide by 10
once, divide by 10 twice, divide by 10 three times. We get to 9.967. So another way of writing
9,967 thousandths, well, that's just going to be 9.967. Or I could literally read
it as 9 and 967 thousands. And that also makes sense. I mean, you could break
this up into 9,000 plus 967. And so 9,000 thousandths
is going to be 9. And then you're going to be
left with the 967 thousandths.