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### Course: Arithmetic > Unit 16

Lesson 2: Multiplying decimals strategies# Multiplying decimals using estimation

Learn all about multiplying decimals by using using estimation. Practice ignoring the decimals first, and multiplying the numbers as wholes. Then, use estimation to find where the decimal should go, ensuring the answer is reasonable. Created by Sal Khan.

## Want to join the conversation?

- Can someone please simplify the process?(3 votes)
- Mmm... I think it's 2.8times 4.73=13.244

473

times 28

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3784

9460

---------

13244

Just do it on a note book, if you do much, I think it's kind of easy. Or... You can think in mind: 3times 5(1 vote)

- Yes. Can someone please simplify the process?(1 vote)
- First, you want to to multiply rhe decimals as if they were whole numbers, so take away the decimal points. Instead of 4.73 times 2.8, you would do 473 times 28. That is 13244. Then, you would round the decimals to whole numbers which would be 5 times 3. That is 15. Then to figure out where the decimal point would go, you would do trial and error by putting the decimal point in every possible place until you find the number that is closest to 15. Hope this helps!(4 votes)

## Video transcript

- [Instructor] So let's
see if we can come up ways to compute what 2.8 times 4.73 is. So pause this video,
and try to work it out. And, actually, I'll give you a hint. Try to figure out, just using the digits, not even paying attention to the decimals, the digits that the product would have, and then use estimation to think about where to place the decimal in your product so you get a reasonable answer. All right, now, let's do this together. So let's just imagine
that we were multiplying these numbers without decimals. So that would be a situation where we would have 473 times 28, and so we could try to compute that. And, so, we could think about
let's multiply everything times the eight, so
three times eight is 24, seven times eight is 56, plus two is 58. And then four times eight
is 32, plus five is 37. And then we could multiply
everything times the two. I'll cross those out so
I don't get confused. Three times two is going to be six, so we have to be very careful, we are now in the tens place,
so we want a zero here, so three times two tens
is going to be six tens. Seven times two is 14. Four times two is eight, plus one is nine. We add everything together, and we get four plus zero is four, eight plus six is 14, and then one plus seven plus four is 12, and then we get one plus three is four, plus nine is equal to 13. So we know that the final
answer has the digits one, three, two, four, four in that order. One, three, two, four, four. So now we have to think about
where would we put a decimal for this to be a reasonable answer? And here's where estimation is useful. We know that 2.8 times 4.73 is going to be roughly equal to what? Well, 2.8 is pretty close to three, so I'll estimate 2.8 as being three. And 4.73 is, if I had to estimate, I would say, "Hey, it'd
be pretty close to five." So this should be pretty
close to three times five, so it should be close to 15. So if I were to put the decimal there, that's way more than 15, so
that doesn't seem reasonable. Even if I were to put the decimal there, 1,324.4 is still way more than 15. If I were to put the decimal there, still way more than 15. If I were to put the decimal there, hey, that actually feels about right. 13 and 244 thousandths is, is approaching 15, it's in the ballpark. And it's actually the closest, 'cause if we were to
put the decimal there, then we go to 1.3244,
so a lot less than 15. So if we want this to
be roughly equal to 15, we definitely would wanna put
the decimal right over there. That is the most reasonable
computation we can do, 'cause we know the digits are going to be one,
three, two, four, four, and this helps us put the decimal. In the future, we're
gonna come up with ways of doing it that where
you don't necessarily have to estimate, but I encourage you, the estimation is always key. If you ever in your life
forget some type of method or process for multiplying decimals, it's the estimation that
allows you to understand whether you're coming up
with a reasonable answer. This is really important, 'cause the decimal, there's a, I remember reading a news
story a couple years ago where someone put in a stock trade where they got the decimal wrong. And because of that, they
essentially sold 10 times as many shares as they were supposed to, and so they lost hundreds
of millions of dollars. So, anyway, decimals are important.