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### Course: 5th grade (Eureka Math/EngageNY) > Unit 1

Lesson 5: Topic E: Multiplying decimals- Estimating with multiplying decimals and whole numbers
- Estimating with multiplying decimals and whole numbers
- Strategies for multiplying decimals and whole numbers
- Multiply whole numbers by 0.1 and 0.01
- Multiplying decimals and whole numbers with visuals
- Multiply decimals and whole numbers visually
- Strategies for multiplying multi-digit decimals by whole numbers
- Multiply whole numbers and decimals
- Estimating decimal multiplication
- Estimating with multiplying decimals
- Represent decimal multiplication with grids and area models
- Understanding decimal multiplication
- Multiplying decimals using estimation
- Understand multiplying decimals
- Developing strategies for multiplying decimals
- Multiply decimals tenths
- Multiplying decimals (no standard algorithm)
- Multiply decimals (up to 4-digit factors)

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# Understanding decimal multiplication

This video introduces multiplying decimals, emphasizing the role of decimal placement in the product. It highlights the usefulness of estimation in simplifying calculations and understanding the relationship between the numbers. Created by Sal Khan.

## Want to join the conversation?

- If you are having a hard time, this is the simplified how-to-do. Just multiply the numbers, count the decimal places, remove them, and when you are done with multiplying, move the number of decimal places you counted to the left. Hope this helps!(19 votes)
- 1:06
**what***does*he mean?(1 vote)- well, he is saying that 76.2 can be rounded to 76 I like to think of it as a whole number so 76.2 becomes 762 and i think to round it to the nearest ten so that be comes 760 the I make it a decimal and were done.(7 votes)

- He is so funny and his videos are so useful!

-JJ.Kijak(0 votes)

## Video transcript

- [Instructor] We are told
that 52 times 762 is equal to 39,624, and then we're
told to match each expression to its product. And these products, this is an exercise on Khan Academy, you can move them around so the product can be matched
to the appropriate expression. So pause this video and see
if you can figure that out. All right, now what you
might have realized is all of these expressions
deal with the same digits as 52 times 762. They just have the decimal
in different places. And so what we can do
is, we can say, hey look, the answer is going to have
the digits three, nine, six, two, four, in that order. And you could see all of
these have the digits three, nine, six, two, four, in that order. And then we can estimate what these expressions should be equal to, what the products should be equal to, to think about the decimal. So this first expression, 0.52 times 76.2, the way I think about
it is 0.52, that's close to 50/100, that's close to a half, and so 76.2, that's close to 76. And so this first expression, this first product should
be roughly half of 76. Half of 76 would be around 38. And so which of these is close to 38? Well this first one is 39.624, so that's actually the closest to 38. The second one is 396. And then we have 3,962. So I like this first one, the 39.624. That feels right. Now the second expression, 0.52 times 762. Well once again, 0.52 is
roughly equal to 50/100, roughly equal to 5/10,
roughly equal to 1/2, and so, and 762, we
could say hey, you know, that's, if we wanna be really rough, really, really approximate it, we could say, hey, it's roughly 800. And so this should be about half of 800, so it should be around 400. And so we actually had
that choice already there. So this would be 396.24. Definitely wouldn't be the the 3,962.4. And so I'm already feeling good that this last choice sits down here. But I can verify it. 5.2, well let's just say that's roughly 5. 762, let's say that's roughly 800. So five times 800, that would be around, that would be 4000. And so we would expect this expression to be close to 4000, and indeed, that's what this choice is. So it turns out that it
was already in the order that we needed it to be, but it's good that we checked on that.