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Current time:0:00Total duration:5:19

Visual understanding of regrouping decimals

CCSS.Math:

Video transcript

what we're going to do in this video is explore place value involving decimals and in particular we're going to think about how you can regroup value from one place to another which is going to be very useful later in your life when you start doing some more arithmetic with decimals so let's first think about what this number is right over here so each square represents a 1 or represents a whole so what number is this well you could see that we have three whole ones so we could write three and then we have right over here Oh a whole is divided into ten equal bars these vertical bars and so each of these are a tenth and four of them are shaded in so it's three ones four tenths and in this this part right over here we've divided a hole into a hundred equal sections it's a 10 by 10 grid and we can see that one two three four five six seven of them are shaded in so this represents seven hundredths so this is three point four seven or three four three and four tenths and seven hundreds or three and forty seven hundredths now what we're going to do is explore how are other ways you can you can put the value into the different places so let me set up a little a little table here I don't think I'm going to need all that space but we have in this first example so we have our ones we have our ones place we have our tenths place and we have our hundreds hundreds hundreds place I had to curve up a little bit and so what we just did is we said hey this was pretty straightforward this was three ones three ones 4/10 and seven hundredths 700s but are there other ways that we could look at it for example is there a way of reimagining this so instead of three ones we have two ones and we still have seven hundredths so how many tenths would we have in order for it to be the same value pause this video and think about that all right we'll do it together and to help us I will put what we had here just now now what's different instead of having three ones we now have two ones so we could say that these are our two ones right over here our two ones we have our seven hundredths right over here so essentially we would have to express all of this in terms of tenths so how would we express it all in terms of tenths well this what we used to be a 1 this is equivalent to 10 tenths let me make that very clear I could see let me see if I could shade this in with that green color so there you go I'm gonna show you with the green color and then let me draw a bunch of lines here to make it very clear so I'm just gonna hand draw it so 1 2 3 4 5 6 7 8 9 and 10 did I do that right 1 2 3 4 5 6 7 8 9 10 and I didn't draw it as straight as I need to it they really should be 10 equal sections but it was hand drawn so I think you understand and so look notice I took the exact same value but I have regrouped I have regrouped this one right over here into tenths and so how many tenths are here well now I have 10 plus 4 tenths so now I have shaded in four teen tents that was interesting let's do another example so now let's imagine another scenario let's imagine a Sarah where we have three ones again but this time instead of having seven hundredths we have 27 hundredths so in that circumstance how many tenths would we have pause this video and see if you can work it through all right well let's get that same number again and now let's think about how we might have to regroup between the places so we have our three ones so that was just like the first case right over there so we have our three ones but now we have 27 hundredths so in addition to these seven hundredths we have to find another 20 hundredths someplace well the most natural place to go would be right over here and hundreds is the same thing as two tenths so what we want to do is we would convert these two tents into hundreds and so let me actually just shade it in a little bit so I'm going to convert this right over here to hundreds and so they did that right one two three four five six seven eight nine ten and so there you have it this Plus this gives us our twenty seven hundredths and so how many tenths do we have left we have two tenths two tenths so in this situation we regrouped to from the tenths place and we express them as hundredths so two tenths became 20 hundredths add it to the seven hundredths that you already have and we now have 27 hundredths hopefully that makes sense