Multiplying decimals
Multiplication 8: Multiplying decimals (Old video) Multiplying decimals (www.khanacademy.org)
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- Welcome to the presentation on multiplying decimals.
- Let's get started.
- So I think you'll find out that multiplying decimals
- is not a lot more difficult than just multiplying regular numbers.
- And I'll show you in a problem.
- Lets say, let me pick some random numbers.
- Let's say I had seven thousand five hundred eighteen.
- Actually, let's make that's seventy-five point one eight.
- Clearly you can tell I'm doing this on the fly.
- Seventy-five point one eight times zero point nine seven.
- So first you look at this problem and you're like, oh boy that's tough.
- These decimals-- I don't even know how to approach it.
- Well this is what you do.
- You ignore the decimals when you start the problem
- and you pretend like it's just a regular multiplication problem.
- And if you ignore the decimals, it would be like I said at the beginning,
- seven thousand five hundred eighteen on top and ninety-seven on the bottom.
- And if that doesn't make sense let me just show you.
- I'm just going to ignore the decimals
- and do this like a normal multiplication problem.
- So normal multiplication.
- I'd start at the ones place right here.
- I'd say seven times eight.
- Well, seven times eight is fifty-six.
- Carry the five.
- Seven times one is seven.
- Plus the five is twelve.
- Two down here.
- Carry the one.
- Seven times five is thirty-five.
- Plus the one is thirty-six.
- Put the six here.
- Carry the three.
- And then seven times seven is forty-nine.
- Plus three is fifty-two.
- So just put fifty-two here.
- So just like normal multiplication
- we just took the ones place right here, the seven.
- So it's actually not the ones,
- but we're ignoring the decimals
- so if there were no decimals this would be the ones place.
- And we're multiplying it by the top number.
- Seven times seven thousand five hundred eighteen is equal to fifty-two thousand six hundred twenty-six.
- And just like regular multiplication, we do the tens place.
- And this isn't really the tens place,
- but if you ignore the decimals it would be.
- And let's cross all this stuff out since we're not using it.
- Nine times eight is seventy-two.
- Carry the seven.
- Nine times one is nine.
- Plus seven is sixteen.
- Carry the one.
- Nine times five is forty-five.
- This is good practice for me, too.
- I haven't done my multiplication tables in a long time.
- Nine times five is forty-five.
- Plus one is forty-six.
- Carry the four.
- Nine times seven is sixty-three.
- Plus four is sixty-seven.
- Now we add.
- So you're probably thinking, boy, what do decimals have to do with this at all?
- I'm just doing a regular multiplication problem.
- And I'll show you.
- Actually the decimals only come in right at the very end.
- So what I do is now I just add like I do a regular level four multiplication problem.
- So I say six plus zero is six.
- Two plus two is four.
- Six plus six is twelve.
- Carry the one.
- One plus two plus six is nine.
- Five plus seven is twelve.
- Carry the one.
- One plus six is seven.
- Okay, so now here's where the decimals come into play.
- And your I think you're going to be shocked by how straightforward this is.
- What I do is I go back to the original problem
- and now I actually pay attention to the decimals.
- And I say, how many total numbers are behind the decimal point?
- Well, there's one number behind the decimal point,
- two numbers behind the decimal point,
- three numbers behind the decimal point,
- four numbers behind the decimal point.
- One, two, three, four.
- So there are four numbers behind the decimal point in the problem I did, and I just count here.
- One, two, three, four.
- The answer will also have four numbers behind the decimal point,
- and that's the answer.
- Seventy-two point nine two four six.
- Now let me ask you a question.
- If I had a zero here,
- would that count as an extra number behind the decimal point?
- Well, it only would have been
- if you actually used the zero in the multiplication.
- Maybe that confuses you.
- What I would recommend,
- if you have any trailing zeros with a decimal like this,
- you should actually just ignore those zeros,
- and then do the problem just the way I did it.
- And remember, that's only for trailing zeros.
- If this was the bottom number then that zero would matter
- because it's not a trailing zero, its actually part of the number.
- Let's do a couple more examples and I think that'll make sense.
- So let's say I had five--
- and I'm going to do a simpler example arithmetically.
- I think it'll help you with some principles.
- If I said five point one zero times one point zero nine.
- So there's two things we could do.
- We could just multiply it the way it is.
- Actually let's do it both ways.
- And I'll show you that you get the same answer whether or not you ignore that zero.
- So in the first case let's not ignore the zero.
- Let's use that zero, even though that trailing zero in the decimal--
- five point one zero is the same thing as five point one.
- But let's use it.
- Nine times zero is zero.
- Nine times one is nine.
- Nine times five is forty-five.
- And in the zeros place you put a zero
- and then zero times everything is zero. Right?
- Zero times zero, zero times one, zero times five.
- Put two zeros here.
- And then one times zero is zero.
- One times one is one.
- And one times five is five.
- And now we add it all.
- We get zero, nine, five, five, five.
- And like we did before, we just count the decimals.
- One, two, three, four.
- So one, two, three, four.
- So the decimal will go here.
- So we got five point five five nine zero as the answer.
- Now what if we did like I was recommending, we actually ignored the zero?
- So I say, And I can actually rewrite it as one point zero nine times five point one.
- Because you know in multiplication order doesn't matter.
- a times b is the same thing as b times a.
- Two times three is the same thing as three times two.
- So one point zero nine times five point one is the same thing as five point one times one point zero nine.
- So let's just multiply this out.
- And notice, these are the same numbers.
- All I did is I took the zero off.
- So, first I just ignore the decimals. I say one times nine is nine.
- One times zero is zero.
- One times one is one.
- Put a zero here.
- Five times nine is forty-five.
- Carry the four.
- Five time zero is zero.
- Plus four is four.
- Five times one is five.
- Now I add.
- Nine, five, five, five.
- Now I'm at the point
- that I can actually pay attention to the decimal points.
- How many numbers are behind the decimals?
- Well, there's one, two, three.
- So I go one, two, three, and put the decimal point right here.
- Notice I got the same exact answer.
- The only difference is that this one had a trailing zero,
- which really doesn't make a number any different.
- I could add a hundred zeros here
- and the number's really not a different number.
- If you were a computer programmer
- or a statistician of some kind, this could be an important number.
- But ignore what I just said.
- But for your purposes, these trailing zeros mean nothing.
- Same way a leading zero actually would mean nothing.
- No one ever does that.
- Let me do-- well, let me see how much time I have.
- I have two more minutes.
- Let me do one more problem just to maybe hit the point home.
- You know, this is really no different than level four multiplication.
- And at the end you just have to count the numbers behind the decimal point.
- So five times five is twenty-five.
- Whoops. Twenty-five.
- I'm already getting messy.
- Carry the two.
- Fve times seven is thirty-five.
- Plus two is thirty-seven.
- Bring down the seven, carry the three.
- Five times zero is zero.
- Plus three.
- So it's three hundred and seventy-five, ignore that blob.
- I'm sorry for being so messy.
- And then you put a zero.
- One times five is five.
- One times seven is seven.
- Ignore that.
- Now we add.
- We say five plus zero is five.
- Seven plus five is twelve.
- One plus three plus seven is eleven.
- So we got our answer,
- now we just have to count the decimals.
- So here we have one, two, three, four,
- five numbers behind the decimal point.
- But in our answer we only have four digits,
- so how can we get five numbers behind the decimal point?
- Well, we start here.
- We say one, two, three, four,
- and we need one more number behind the decimal point,
- so we add a zero here.
- And then we put the decimal point.
- See what I just did?
- We had to have five numbers behind the decimal point.
- And we only had four numbers in the answer.
- So I added a leading zero and then put the decimal point.
- And now we have five numbers behind the decimal point.
- And I've shown you a very mechanical way of doing this.
- Hopefully in the future I can give you a seminar on actually
- why this method of counting the numbers behind the decimal points actually works.
- But I think you are ready to try some problems on multiplying decimals.
- Have fun!
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
|
Have something that's not a question about this content? |
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.