Multiplying Decimals - By Anywhere Math
Transcript
00:0-1 | While in your room is 5.6 m by 3.2 m | |
00:04 | . A small can of paint will cover about 20 | |
00:08 | m2 . Do you have enough paint to paint your | |
00:11 | wall ? Welcome to anywhere . Math . I'm Jeff | |
00:31 | , Jacobson . And today we're gonna talk about multiplying | |
00:34 | decimals . All right , so let's talk about that | |
00:37 | wall . Uh , it was 5.6 m by 3.2 | |
00:41 | m . So if you think drawing a picture , | |
00:46 | You know , this is gonna be about 5.6 m | |
00:49 | by 3.2 m , we want to know if we're | |
00:53 | gonna have enough paint . So what we need to | |
00:54 | find is area . That's what we're covering with the | |
01:00 | paint . So to do that , we're just gonna | |
01:02 | multiply right ? Lake times with uh , so 5.6 | |
01:05 | times 3.2 5.6 times 3.2 . Now , if we | |
01:14 | were going to estimate this , that would be about | |
01:16 | six , that would be about three . six times | |
01:23 | 3 is about 18 . So hopefully If our estimation | |
01:28 | is somewhere accurate , uh we should have enough . | |
01:31 | So let's see , let's just multiply six times two | |
01:34 | is 12 . 10 plus one is 11 0 . | |
01:40 | Uh 18 . Another 1 , 15 plus one is | |
01:44 | 16 2971 . Now , if you're thinking well where | |
01:52 | This is decimals , right , where's my decimal point | |
01:54 | gonna go ? You think it should be close to | |
01:56 | 18 ? That's what point goes there , 17.92 . | |
02:01 | Don't forget your units . It was meters times meters | |
02:04 | . So that becomes meters squared , which makes sense | |
02:07 | for area . So 17.92 m squared . The small | |
02:13 | can of paint could cover 20 m squared or 20 | |
02:16 | m2 . So do we have enough ? And the | |
02:18 | answer is yeah . Yes . Okay , so let's | |
02:23 | try another example . All right . Here's example 1 | |
02:26 | , 6 times 3.91 . Now , when you're dealing | |
02:30 | with decimals , it's always a good idea to estimate | |
02:34 | . And the reason is because it can be very | |
02:36 | easy to put the decimal point in the wrong spot | |
02:40 | , which completely changes your answer . Uh So if | |
02:43 | you estimate that will help kind of catch those heirs | |
02:46 | . So if we're going to estimate this would be | |
02:53 | six is okay 3.91 , we can just round up | |
02:57 | to four . So we're thinking Our products should be | |
03:02 | around 24 . So let's see now when you're multiplying | |
03:07 | with decimals , the trick is to treat it like | |
03:11 | the decimal isn't there set up the problem like you | |
03:14 | would a normal multiplication problems . So what I'm saying | |
03:17 | is Don't think of this as 3.91 . Imagine it's | |
03:21 | just 391 Times six . Well if it was that | |
03:26 | You would put the 391 mm on top , Multiply | |
03:32 | it by six . That's how you would set it | |
03:35 | up . Right . Um And we can do that | |
03:38 | because order doesn't matter with multiplication because of the community | |
03:41 | of property . So we can do that once you | |
03:43 | set it up like that , then go ahead and | |
03:45 | put the decimal point back in . Just don't forget | |
03:49 | that . And now we just multiply like normal . | |
03:51 | Um that's gonna be 66 times nine is 54 carry | |
03:57 | the 56 times three is 18 plus five is 23 | |
04:02 | . Now this is the last step and it's really | |
04:07 | important . Where does the decimal point go in ? | |
04:09 | Our answer ? Can all you have to do ? | |
04:13 | Yeah is look at how many places you have after | |
04:16 | the decimal points in your problem . So here we've | |
04:21 | got the nine and the one two places after the | |
04:25 | decimal and 3.91 . So that's two six . Does't | |
04:29 | have any right . The decimal point if we want | |
04:32 | it would be here . There's nothing over there so | |
04:36 | that's going to be zero . So in our answer | |
04:40 | we need two decimal places . Yeah . Okay . | |
04:48 | So yeah , 12 The decimal point goes there and | |
04:55 | that is our product . That's our answer . 23.46 | |
05:00 | . And let's check , does that make sense with | |
05:03 | our estimate ? Yeah , it's really , really close | |
05:05 | so we know we're good . Okay , let's try | |
05:08 | another one . Another example Here is example , # | |
05:13 | two , times 100 . Um When you're multiplying by | |
05:17 | powers of 10 , Uh like 100 is it's 10 | |
05:22 | times 10 or 10 squared ? There's a really nice | |
05:27 | shortcut that you can make if you remember our whole | |
05:30 | number system is Base 10 . It's based on powers | |
05:34 | of 10 . So if you think well yeah , | |
05:39 | Take it simpler . Well what's two times 10 ? | |
05:42 | Well that's just 20 two times 100 adds 200 . | |
05:48 | two times 1000 . That's 2000 . Okay , um | |
05:54 | That's very simple because it's just a whole number . | |
05:56 | All you do is add zeros at the end , | |
05:58 | right ? You do the one times the two and | |
06:00 | then add however many zeros you have . Uh But | |
06:03 | you can also think of it , well if there | |
06:05 | was a decimal here , where would it be ? | |
06:09 | Well with whole numbers we can put a decimal right | |
06:11 | after . Okay . And now from here to here | |
06:18 | , what happened to the decimal ? It went from | |
06:20 | here over one And you just filled in a zero | |
06:25 | Here . It was times 100 . So we're moving | |
06:28 | it twice . Right , filled in those zeros here | |
06:32 | times 1000 . You're moving the desperate 10000.3 times When | |
06:37 | you're multiplying by powers of 10 , you're moving the | |
06:40 | decimal point to the right And you just got to | |
06:43 | think well how many powers of 10 , 10 ? | |
06:45 | You're moving at once ? 10 is the same as | |
06:49 | 10 to the first power . 100 is 10 square | |
06:54 | to your moving it twice . 1000 is 10 cubed | |
06:58 | . You're moving it three times . You can also | |
07:00 | think how many zeros are there , That's how many | |
07:02 | times you're moving it . So with that in mind | |
07:07 | this problem becomes much , much easier . I'm multiplying | |
07:11 | by a power of 10 . I'm gonna move it | |
07:14 | to the right because I'm multiplying And there's two zeros | |
07:18 | or I can think of that as 10 squared to | |
07:21 | the power of two . So I'm going to move | |
07:23 | it once twice . So that becomes 135 . Right | |
07:31 | ? Very simple . Here's something to try on your | |
07:33 | own . All right . Here's our last example 3.1 | |
07:41 | times 0.05 . Now , if you remember at the | |
07:45 | beginning of the video I said when you're multiplying with | |
07:48 | death was pretend the decimal points aren't there ? And | |
07:52 | set up the problem like that . So I'm not | |
07:55 | going to think of this as three point when I'm | |
07:56 | going to think of it as 31 times 005 . | |
08:01 | Um Now there's a couple ways I could put the | |
08:05 | 31 on top or I could put the 005 on | |
08:09 | top . Me personally I like to do whichever ones | |
08:13 | have the most digits . I like to put that | |
08:15 | on top But it doesn't matter . You can do | |
08:17 | it either way you want . So I'm gonna set | |
08:19 | this up at 005 times 31 . Okay , pretend | |
08:28 | the decimal points aren't there ? And set it up | |
08:29 | that way . Now that I've set it up , | |
08:32 | I'm going to put them back so I don't forget | |
08:34 | . That's what point is there ? That's my point | |
08:36 | is there . Now you'll notice these decimal points aren't | |
08:42 | lined up . And that is the main difference between | |
08:46 | adding subtracting decimals . Where the decimal points have to | |
08:49 | be lined up and multiplying with decimals where they don't | |
08:54 | . Okay , that's the main thing to remember . | |
08:56 | So you should write that down when you're multiplying with | |
08:59 | decimals . The decimal points do not have to be | |
09:02 | lined up . Okay , so that's how we're setting | |
09:05 | it up and now I just multiply One times five | |
09:08 | is 5 . That's going to be 00 at zero | |
09:13 | . Three times five is 15 carry the one that | |
09:16 | zero plus one is 10 Add them up . I | |
09:21 | get 5510 . Now the last step Is to count | |
09:30 | my decimal places . This here , 0.05 has to | |
09:35 | that has won Adam together . My answer should have | |
09:39 | three decimal places . So 123 My aunt , my | |
09:45 | decimal point goes right there And that is my answer | |
09:50 | . Now . If I want to check if I | |
09:52 | want to estimate , well if I'm going to estimate | |
09:55 | that would be round of three times that's very close | |
09:59 | to zero . So three times zero is zero . | |
10:01 | Is my answer pretty close to zero . Yeah it | |
10:05 | is . So that's the last example Again , remember | |
10:09 | when you're multiplying decimals do not line them up ? | |
10:12 | Sometimes they will line up just you know because they | |
10:15 | have the same decimal places but they don't need to | |
10:18 | be okay so that's the main difference . Here's some | |
10:21 | more to try and europe . Thank you for watching | |
10:28 | . And as always if you like this video please | |
10:30 | subscribe . |
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