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Decimal Squares - Interactive Games - References

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Includes Decimal Squares, a program for teaching all decimal concepts, and also references, links, research statements, and interactive games for learning about decimals.

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Interactive Math Lesson | Place Value Decimals to Thousandths

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"I Know It" is an elementary math practice website. Try out this fifth-grade math lesson to practice place value with decimals to thousandths with your class today!

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5) Multiplying whole numbers and multiplying by decimal numbers

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5) Multiplying whole numbers and multiplying by decimal numbers

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Let's now see if we can divide into larger numbers. And just as a starting point, in order to divide into larger numbers, you at least need to know your multiplication tables from the 1-multiplication tables all the way to, at least, the 10-multiplication. So all the way up to 10 times 10, which you know is 100. And then, starting at 1 times 1 and going up to 2 times 3, all the way up to 10 times 10. And, at least when I was in school, we learned through 12 times 12. But 10 times 10 will probably do the trick. And that's really just the starting point. Because to do multiplication problems like this, for example, or division problems like this. Let's say I'm taking 25 and I want to divide it by 5. So I could draw 25 objects and then divide them into groups of 5 or divide them into 5 groups and see how many elements are in each group. But the quick way to do is just to think about, well 5 times what is 25, right? 5 times question mark is equal to 25. And if you know your multiplication tables, especially your 5-multiplication tables, you know that 5 times 5 is equal to 25. So something like this, you'll immediately just be able to say, because of your knowledge of multiplication, that 5 goes into 25 five times. And you'd write the 5 right there. Not over the 2, because you still want to be careful of the place notation. You want to write the 5 in the ones place. It goes into it 5 ones times, or exactly five times. And the same thing. If I said 7 goes into 49. That's how many times? Well you say, that's like saying 7 times what-- you could even, instead of a question mark, you could put a blank there --7 times what is equal to 49? And if you know your multiplication tables, you know that 7 times 7 is equal to 49. All the examples I've done so far is a number multiplied by itself. Let me do another example. Let me do 9 goes into 54 how many times? Once again, you need to know your multiplication tables to do this. 9 times what is equal to 54? And sometimes, even if you don't have it memorized, you could say 9 times 5 is 45. And 9 times 6 would be 9 more than that, so that would be 54. So 9 goes into 54 six times. So just as a starting point, you need to have your multiplication tables from 1 times 1 all the way up the 10 times 10 memorized. In order to be able to do at least some of these more basic problems relatively quickly. Now, with that out of the way, let's try to do some problems that's might not fit completely cleanly into your multiplication tables. So let's say I want to divide-- I am looking to divide 3 into 43. And, once again, this is larger than 3 times 10 or 3 times 12. Actually, look. Well, let me do another problem. Let me do 3 into 23. And, if you know your 3-times tables, you realize that there's 3 times nothing is exactly 23. I'll do it right now. 3 times 1 is 3. 3 times 2 is 6. Let me just write them all out. 3 times 3 is 9, 12, 15, 18, 21, 24, right? There's no 23 in the multiples of 3. So how do you do this division problem? Well what you do is you think of what is the largest multiple of 3 that does go into 23? And that's 21. And 3 goes into 21 how many times? Well you know that 3 times 7 is equal to 21. So you say, well 3 will go into 23 seven times. But it doesn't go into it cleanly because 7 times 3 is 21. So there's a remainder left over. So if you take 23 minus 21, you have a remainder of 2. So you could write that 23 divided by 3 is equal to 7 remainder-- maybe I'll just, well, write the whole word out --remainder 2. So it doesn't have to go in completely cleanly. And, in the future, we'll learn about decimals and fractions. But for now, you just say, well it goes in cleanly 7 times, but that only gets us to 21. But then there's 2 left over. So you can even work with the division problems where it's not exactly a multiple of the number that you're dividing into the larger number. But let's do some practice with even larger numbers. And I think you'll see a pattern here. So let's do 4 going into-- I'm going to pick a pretty large number here --344. And, immediately when you see that you might say, hey Sal, I know up to 4 times 10 or 4 times 12. 4 times 12 is 48. This is a much larger number. This is way out of bounds of what I know in my 4-multiplication tables. And what I'm going to show you right now is a way of doing this just knowing your 4-multiplication tables. So what you do is you say 4 goes into this 3 how many times? And you're actually saying 4 goes into this 3 how many hundred times? So this is-- Because this is 300, right? This is 344. But 4 goes into 3 no hundred times, or 4 goes into-- I guess the best way to think of it --4 goes 3 0 times. So you can just move on. 4 goes into 34. So now we're going to focus on the 34. So 4 goes into 34 how many times? And here we can use our 4-multiplication tables. 4-- Let's see, 4 times 8 is equal to 32. 4 times 9 is equal to 36. So 4 goes into 34-- 30-- 9 is too many times, right? 36 is larger than 34. So 4 goes into 34 eight times. There's going to be a little bit left over. 4 goes in the 34 eights times. So let's figure out what's left over. And really we're saying 4 goes into 340 how many ten times? We're actually saying 4 goes into 340 eighty times. Because notice we wrote this 8 in the tens place. But just for our ability to do this problem quickly, you just say 4 goes into 34 eight times, but make sure you write the 8 in the tens place right there. 8 times 4. We already know what that is. 8 times 4 is 32. And then we figure out the remainder. 34 minus 32. Well, 4 minus 2 is 2. And then these 3's cancel out. So you're just left with a 2. But notice we're in the tens column, right? This whole column right here, that's the tens column. So really what we said is 4 goes into 340 eighty times. 80 times 4 is 320, right? Because I wrote the 3 in the hundreds column. And then there is-- and I don't want to make this look like a-- I don't want to make this look like a-- Let me clean this up a little bit. I didn't want to make that line there look like a-- when I was dividing the columns --to look like a 1. But then there's a remainder of 2, but I wrote the 2 in the tens place. So it's actually a remainder of 20. But let me bring down this 4. Because I didn't want to just divide into 340. I divided into 344. So you bring down the 4. Let me switch colors. And then-- So another way to think about it. We just said that 4 goes into 344 eighty times, right? We wrote the 8 in the tens place. And then 8 times 4 is 320. The remainder is now 24. So how many times does 4 go into 24? Well we know that. 4 times 6 is equal to 24. So 4 goes into 24 six times. And we put that in the ones place. 6 times 4 is 24. And then we subtract. 24 minus 24. That's-- We subtract at that stage, either case. And we get 0. So there's no remainder. So 4 goes into 344 exactly eighty-six times. So if your took 344 objects and divided them into groups of 4, you would get 86 groups. Or if you divided them into groups of 86, you would get 4 groups. Let's do a couple more problems. I think you're getting the hang of it. Let me do 7-- I'll do a simple one. 7 goes into 91. So once again, well, this is beyond 7 times 12, which is 84, which you know from our multiplication tables. So we use the same system we did in the last problem. 7 goes into 9 how many times? 7 goes into 9 one time. 1 times 7 is 7. And you have 9 minus 7 is 2. And then you bring down the 1. 21. And remember, this might seem like magic, but what we really said was 7 goes into 90 ten times-- 10 because we wrote the 1 in the tens place --10 times 7 is 70, right? You can almost put a 0 there if you like. And 90 with the remainder-- And 91 minus 70 is 21. So 7 goes into 91 ten times remainder 21. And then you say 7 goes into 21-- Well you know that. 7 times 3 is 21. So 7 goes into 21 three times. 3 times 7 is 21. You subtract these from each other. Remainder 0. So 91 divided by 7 is equal to 13. Let's do another one. And I won't take that little break to explain the places and all of that. I think you understand that. I want, at least, you to get the process down really really well in this video. So let's do 7-- I keep using the number 7. Let me do a different number. Let me do 8 goes into 608 how many times? So I go 8 goes into 6 how many times? It goes into it 0 time. So let me keep moving. 8 goes into 60 how many times? Let me write down the 8. Let me draw a line here so we don't get confused. Let me scroll down a little bit. I need some space above the number. So 8 goes into 60 how many times? We know that 8 times 7 is equal to 56. And that 8 times 8 is equal to 64. So 8 goes into-- 64 is too big. So it's not this one. So 8 goes into 60 seven times. And there's going to be a little bit left over. So 8 goes into 60 seven times. Since we're doing the whole 60, we put the 7 above the ones place in the 60, which is the tens place in the whole thing. 7 times 8, we know, is 56. 60 minus 56. That's 4. We could do that in our heads. Or if we wanted, we can borrow. That be a 10. That would be a 5. 10 minus 6 is 4. Then you bring down this 8. 8 goes into 48 how many times? Well what's 8 times 6? Well, 8 times 6 is exactly 48. So 8 times-- 8 goes into 48 six times. 6 times 8 is 48. And you subtract. We subtracted up here as well. 48 minus 48 is 0. So, once again, we get a remainder of 0. So hopefully, that gives you the hang of how to do these larger division problems. And all we really need to know to be able to do these, to tackle these, is our multiplication tables up to maybe 10 times 10 or 12 times 12.

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Intro to long division (remainders) (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Let's take 63 and divide it by 35. So the first thing that we might say is, OK, well, 35 doesn't go into 6. It does go into 63. It goes into 63 one time, because 2 times 35 is 70, so that's too big. So it goes one time. So let me write that. 1 times 35 is 35. And then if we were to subtract and we can regroup up here, we can take a 10 from the 60, so it becomes a 50, give that 10 to the 3, so it becomes a 13. 13 minus 5 is 8. 5 minus 3 is 2. So you could just say, hey, 63 divided by 35-- let me write this. You could say 63 divided by 35 is equal to 1 remainder 28. But this isn't so satisfying. We know that the real answer is going to be one point something, something, something. So what I want to do is keep dividing. I want to divide this thing completely and see what type of a decimal I actually get. And to do that, I essentially have to add a decimal here and then just keep bringing down decimal places to the right of the decimal. So 63 is the exact same thing as 63.0, and I could add as many zeroes as I might want to add here. So what we could do is we just make sure that this decimals right over there, and we can now bring down a zero from the tenths place right over here. And you bring down that zero, and now we ask ourselves, how many times does 35 go into 280? And, as always, this is a bit of an art when you're dividing a two-digit number into a three-digit number. So let's see, it's definitely going to be-- if I were to say-- so 40 goes into 280 seven times. 30 goes into 280 about nine times. It's going to be between 7 and 9, so let's try 8. So, let's see what 35 times 8 is. 35 times 8. 5 times 8 is 40, 3 times 8 is 24, plus 4 is 28. So it actually works out perfectly. So 35 goes into 280 exactly eight times. 8 times 5, we already figured it out. 8 times 35 is exactly 280, and we don't have any remainder now, so we don't have to bring down any more of these zeroes. So now we know exactly that 63 divided by 35 is equal to exactly 1.8.

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Dividing whole numbers to get a decimal (video) | Khan Academy

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Let's take 63 and divide it by 35. So the first thing that we might say is, OK, well, 35 doesn't go into 6. It does go into 63. It goes into 63 one time, because 2 times 35 is 70, so that's too big. So it goes one time.

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We now have the general tools to really tackle any multiplication problems. So in this video I'm just going to do a ton of examples. So let's start off with-- and I'll start in yellow. Let's start off with 32 times 18. Say 8 times 2 is 16. Well, I'll do it in our head this time because you always don't have all this space to work with. So 8 times 2 is 16. Put the 1 up there. 8 times 3 is 24. 24 plus 1 is 25. So 8 times 32 was 256. Now we're going to have to multiply this 1, which is really a 10, times 32. I'll underline it with the orange. 1 times 2-- oh, we have to be very careful here. 1 times 2 is 2. So you might say hey, let me stick a 2 down there. Remember, this isn't a 1. This is a 10, so we have to stick a 0 there to remember that. So 10 times 2 is 20. Or you say 1 times 2 is 2, but you're putting it in the 2's place, so you still get 20. So 10 times 2 is 20. It works out. Then 1 times 3. And we have to be very careful. Let's get rid of what we had from before. 1 times 3 is 3. There's nothing to add here, so you just get a 3. And so you get 10 times 32 is 320. This 1 right here, that's a 10. 10 plus 8 is 18. So now we just add up the two numbers. You add them up. 6 plus 0 is 6. 5 plus 2 is 7. 2 plus 3 is 5. Let's keep going. Let's do 99 times 88. So a big number. 8 times 9 is 72. Stick the 7 up there. And then you have 8 times 9 again. 8 times 9 is 72, but now you have the 7 up here. So 72 plus 7 is 79. Fair enough. Now we're done with this. Let's just delete it just so that we don't get confused in our next step. In our next we're going to multiply this 8 now times 99. But this 8 is an 80. So let's stick a 0 down there. 8 times 9 is 72. Stick a 7 up there. Then 8 times 9 is 72. Plus 7 is 79. 2 plus 0 is 2. Let me switch colors. 9 plus 2 is 11. Carry the 1. 1 plus 7 is 8. 8 plus 9 is 17. Carry the 1. 1 plus 7 is 8. 8,712. Let's keep going. Can't do enough of these. All right, 53 times 78. I think you're getting the hang of it now. Let's multiply 8 times 53 first. So 8 times 3 is 24. Stick the 2 up there. 8 times 5 is 40. 40 plus 2 is 42. Now we're going to have to deal with that 7 right there, which is really a 70. So we got to remember to put the 0 there. 7 times 3, and let's get rid of this. Don't want to get confused. 7 times 3 is 21. Put the 1 there and put the 2 up here. 7 times 5 is 35. Plus 2 is 37. Now we're ready to add. 4 plus 0 is 4. 2 plus 1 is 3. 4 plus 7 is 11. Carry the 1. 1 plus 3 is 4. 4,134. Let's up the stakes a little bit. So let's say I had 796 times 58. Let's mix it up well. All right, so first we're just going to multiply 8 times 796. And notice, I've thrown in an extra digit up here. So 8 times 6 is 48. Put the 4 up there. 8 times 9 is 72. Plus 4 is 76. And then 8 times 7 is 56. 56 plus 7 is 63. I'm sure I'll make a careless mistake at some point in this video. And the goal for you is to identify if and when I do. All right, now we're ready, so we can get rid of these guys up here. Now we can multiply this 5, which is in the 10's place. It's really a 50. Times this up here. Because it's a 50 we stick a 0 down there. 5 times 6 is 30. Put the 0 there, put the 3 up there. 5 times 9 is 45. Plus the 3 is 48. 5 times 7 is 35. Plus 4 is 39. Now we're ready to add. 8 plus 0 is 8. 6 plus 0 is 6. 3 plus 8 is 11. 1 plus 6 is 7. 7 plus 9 is 16. And then 1 plus 3 is 4. So 796 times 58 is 46,168. And that sounds about right because 796-- it's almost 800. You know, which is almost 1,000. So if we multiplied 1,000 times 58 we'd get 58,000. But we're multiplying something a little bit smaller than 1,000 times 58, so we're getting something a little bit smaller than 58,000. So the number is in the correct ballpark. Now let's do one more here where I'm really going to step up the stakes. Let's do 523 times-- I'm going to do a three-digit number now. Times 798. That's a big three-digit number. But it's the same exact process. And once you kind of see the pattern you say, hey, this'll apply to any number of digits times any number of digits. It'll just start taking you a long time and your chances of making a careless mistake are going to go up, but it's the same idea. So we start with 8 times 523. 8 times 3 is 24. Stick the 2 up there. Now 8 times 2 is 16. 16 plus 2 is 18. Put the 1 up there. 8 times 5 is 40. Plus 1 is 41. So 8 times 523 is 4,184. We're not done. We have to multiply times the 90 and by the 700. So let's do the 90 right there. So it's a 90, so we'll stick a 0 there. It's not a 9. And let's get rid of these guys right there. 9 times 3 is 27. 9 times 2 is 18. 18 plus 2 is 20. And then we have 9 times 5 is 45. 45 plus 2 is 47. I don't want to write that thick. 47. Let me make sure I did that one right, and let's just review it a little bit. 9 times 3 was 27. We wrote the 7 down here and put the 2 up there. 9 times 2 is 18. We added 2 to that, so we wrote 20. Wrote the 0 down there and the 2 up there. The 9 times 5 was 45. Plus 2 is 47. You really have to make sure you don't make careless mistakes with these. Then finally, we have to multiply the 7, which is really a 700 times 523. When it was just an 8 we just started multiplying here. When it was a 90, when we were dealing with the 10's place, we put a 0 there. Now that we're dealing with something that's in the 100's, we're going to put two 0's there. And so you have 7-- and let's get rid of this stuff. That'll just mess us up. 7 times 3 is 21. Put the 1 there. Stick the 2 up there. 7 times 2 is 14. 14 plus our 2 is 16. Put the 1 up there. 7 times 5 is 35. Plus 1 is 36. And now we're ready to add. And hopefully we didn't make any careless mistakes. So 4 plus 0 plus 0. That's easy. That's 4. 8 plus 7 plus 0. That's 15. Carry the 1. 1 plus 1 plus 1 is 3. 4 plus 7 plus 6. That's what's? 4 plus 6 is 10. It's 17. And then we have 1 plus 4 is 5. 5 plus 6 is 11. Carry the 1. 1 plus 3 is 4. So 523 times 798 is 417,354. Now we can even check to make sure. And so this is the moment of truth. Let's see if we have-- let's see. 523 times 798. There you go. Moment of truth. I don't have to re-record this video. It's 417,354. But we did it without the calculator, which is the important point.

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Multiplying multi-digit numbers (video) | Khan Academy

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We now have the general tools to really tackle any multiplication problems. So in this video I'm just going to do a ton of examples. So let's start off with-- and I'll start in yellow. Let's start off with 32 times 18. Say 8 times 2 is 16.

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- [Instructor] So right over here we wanna compute what three times 0.25 or three times 25 hundredths is. And so I encourage you to pause the video and see if you can figure this out. Alright, now let's work through this together. And in this video, we're gonna explore multiple strategies. In the future, we're going to show you what's called the standard strategy, which you might use a lot, but the strategies we're gonna look at in this video are actually very helpful for understanding what multiplying decimals actually means, how it relates to multiplying fractions, as often the way that people, even people who have a lot of math behind them, how they actually multiply decimals. So here, three times 25 hundredths. There's a couple of ways to think about it. One way is to say, hey, this is the same thing as three times, and I'm just gonna write it a different way. 25 hundredths, hundredths. If I have three times 25 of something, what is it going to be? Well, what's three times 25? Let's see. Two times 25 is 50, three times 25 is 75. So it's going to be 75, and I'm multiplying, not just three times 25, I'm multiplying three times 25 hundredths. Instead of 25 hundredths, I'm gonna have 75, 75 hundredths. Written out in words, this would be 75 hundredths. How would we write that as a decimal? That is the same thing as this, 75 hundredths. Another way to conceptualize this, to think about what this is, is if we were to write three times, we could write it as a fraction. We could write 25/100. This is another way of writing 25 hundredths. These are all equivalent. What is three times 25/100? Same idea. This is going to be equal to, you could say this is 25/100 plus 25/100 plus 25/100. This is going to be 75 hundredths, which once again is 0.75. If you wanted to more formally view it as fraction multiplication, you could view it as 3/1 times 25/100, and you multiply the numerators, you get 75, you multiply the denominators, you get 100. Either way, in all of these situations, you're gonna get 75 hundredths. Or, another way to think about it, is hey look, this thing right over here, this 25/100, this is the same thing as 1/4. So you could view this as three times 1/4. In fact, this is a decimal that it's good to recognize that this is the same thing as 1/4. So you could view this as three times 1/4, or 3/4, this is a fourth right here, 1/4 could be viewed as a fourth, so this is going to be equal to 3/4, three over four, 3/4. All of these are equivalent. If someone wanted it written out as a decimal, you could, you might know that 3/4 can be expressed as 75 hundredths, which in general, is a good thing to know. Now let's tackle slightly more complicated examples. Let's say we wanted to figure out, we wanted to figure out what 0.4 times zero, let me just do this in a new color, times 0.3 is going to be equal to. Pause the video and see if you can compute this, and I'll give you a hint, see if you can express these as fractions. What we have here in white, we could read this as four tenths, and we could write it as a fraction, as 4/10, and we're gonna multiply that by what we have over here. This is three tenths, three tenths, which we could write as a fraction as 3/10, and so you could view this as 4/10 of 3/10 or 3/10 of 4/10, but we're multiplying these fractions, which we've seen before in other videos. What's going to happen? Well, if we multiply the numerator we get 12, or the numerators. We multiply the denominators, you get 100. So you get 12 hundredths. If you wanted to write that as a decimal, it would be 0.12, 12 hundredths. You might notice something interesting here, and you'll see this more and more as you learn the standard method. 12 is four times three is 12, but now I have two digits behind the decimal, but notice, I have one digit behind the decimal here, one digit behind the decimal here, for a total of two digits behind the decimal. I'm giving you a little bit of a hint about where we're going, but the important thing for this video is to recognize that you can re-express each of these as fractions, and then multiply the fractions to get something expressed in terms of hundredths, and then express that as a decimal.

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Developing strategies for multiplying decimals (video) | Khan Academy

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Instructor] So right over here we wanna compute what three times 0.25 or three times 25 hundredths is. And so I encourage you to pause the video and see if you can figure this out. Alright, now let's work through this together. And in this video, we're gonna explore multiple strategies.

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6) Divide whole numbers and decimal numbers to thousandths

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6) Divide whole numbers and decimal numbers to thousandths

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5) Multiply whole numbers and decimal numbers to thousandths

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5) Multiply whole numbers and decimal numbers to thousandths

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Mental Math - work with fraction and decimal numbers

Common Core Connection for Grades 4+

Compare two fractions with different numerators and different denominators.
Use decimal notation for fractions with denominators 10 or 100.
Compare two decimals to hundredths by reasoning about their size.
Understand addition/subtraction of fractions as joining/separating parts of the same whole.

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Number Conundrum Decimals | Math Playground

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Mental Math - work with fraction and decimal numbers Common Core Connection for Grades 4+ Compare two fractions with different numerators and different denominators. Use decimal notation for fractions with denominators 10 or 100. Compare two decimals to hundredths by reasoning about their size. Understand addition/subtraction of fractions as joining/separating parts of the same whole.

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Ordering decimals can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no!

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The trick is to get rid of the decimal point from the number we are dividing by.

How? We can "shift the decimal point" out of the way by multiplying by 10, as many times as we need to.

But we must do the same thing to both numbers in the division.

Example: 15 divided by 0.2

Let us multiply the 0.2 by 10, which shifts the decimal point out of the way:

0.2 × 10 = 2

But we must also do it to the 15:

15 × 10 = 150

So 15 ÷ 0.2 has become 150 ÷ 2 (they are both 10 times larger):

150 ÷ 2 = 75

And so the answer is:

15 ÷ 0.2 = 75

The number we divide by is called the divisor.

To divide decimal numbers:

Multiply the divisor by as many 10's as necessary until we get a whole number.
Remember to multiply the dividend by the same number of 10's.

To multiply by 10 it is easier to just "shift the decimal":

Example: Divide 6.4 by 0.4

Let us just shift the decimal point one space for both:

move 1

6.4 64

0.4 4

move 1

6.4/0.4 is exactly the same as 64/4,
as we moved the decimal point of both numbers.

Now we can calculate:

64 / 4 = 16

So the answer is:

6.4 / 0.4 = 16

Are there really 16 lots of 0.4 in 6.4? Let's see:

For harder questions we may need to use Long Division:

Example: Divide 0.539 by 0.11

Move the decimal point so the divisor (0.11) is a whole number:

move 2 spaces

0.539 5.39 53.9

0.11 1.1 11

move 2 spaces

But what about 53.9? It still has a decimal point.

Well, we can ignore the decimal point in the dividend so long as we remember to put it back later. First we do the calculation without the decimal point:

Now put the decimal point in the answer directly above the decimal point in the dividend:

Another example:

Example: Divide 9.1 by 7

We don't need to shift the decimal point at all, as the divisor (7) is already a whole number.

Ignore the decimal point in the dividend and use Long Division:

Put the decimal point in the answer directly above the decimal point in the dividend:

The answer is 1.3

Animations

Have a look at these Decimal Division Animations for further help.

As a final check we can put our "common sense" hat on and think "is that the right size?", because we don't want to pay ten times too much for anything, nor do we want to get only one-tenth of what we need!

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The trick is to get rid of the decimal point from the number we are dividing by. How? We can "shift the decimal point" out of the way by multiplying by 10, as many times as we need to. But we must do the same thing to both numbers in the division.

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To add decimals, follow these steps:

Write down the numbers, one under the other, with the decimal points lined up

Put in zeros so the numbers have the same length (see below for why that is OK)

Then add using column addition, remembering to put the decimal point in the answer

Example: Add 1.452 to 1.3

Example: Add 3.25, 0.075 and 5

That's all there is to it - just remember to line up the decimals, pad with zeros, then add normally.

Subtracting

To subtract, follow the same method: line up the decimals, then subtract.

Example: What is 7.368 − 1.15 ?

To check we can add the answer to the number subtracted:

Example: Check that 7.368 minus 1.15 equals 6.218

Let us try adding 6.218 to 1.15

It matches the number we started with, so it checks out.

Putting In Zeros

Why can we put in extra zeros?

A zero is really saying "there is no value at this decimal place".

In a number like 10, the zero is saying "no ones"

In a number like 2.50 the zero is saying "no hundredths"

So it is safe to take a number like 2.5 and make it 2.50 or 2.500 etc

But DON'T take 2.5 and make it 20.5, that is plain wrong.

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To add decimals, follow these steps: Write down the numbers, one under the other, with the decimal points lined up Put in zeros so the numbers have the same length (see below for why that is OK) Then add using column addition, remembering to put the decimal point in the answer That's all there is to it - just remember to line up the decimals, pad with zeros, then add normally.

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How to Multiply Decimals

Just follow these steps:

Multiply normally, ignoring the decimal points.

Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.

How Does It Work?

Because when you multiply without the decimal point, you are really shifting the decimal point to the right to get it out of the way:

Original: 1 Move: 2 Moves: 3 Moves:

0.03 × 1.1

0.3 × 1.1

3. × 1.1

3. × 11.

Then we do the (now easy) multiplication:

3. × 11. = 33.

But remember, we did 3 Moves of the decimal point, so we need to undo that:

3 Moves: 2 Moves: 1 Move: Correct

33. 3.3 0.33 0.033

Here are some more examples:

Common Sense

As a final check you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor get only one-tenth of what you need!

And that's all.

Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.

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Just follow these steps: Multiply normally, ignoring the decimal points. Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined. In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.

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Tim and Moby estimate that this movie on rounding and practical math is only about three minutes long.

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The decimal system represents a hundredth or even more than a thousandth of a whole--because sometimes things are just way teenier than one!