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# Rounding to the nearest 10 on the number line

CCSS.Math:

## Video transcript

in this video we're going to be doing some rounding which you're probably not familiar with just yet but you'll see that it's pretty straight forward and we're going to start by rounding to the nearest ten so the first question is what is rounding and why is it even useful well let's say that you have the number 37 it's a fine number but let's say that you have to do some math with the number 37 and you can do a lot of math with the number 37 but let's say you just want to estimate what something might be let's say that someone says hey I have 37 pickles and you have 39 pickles roughly how many do we have together we don't have to have it down to the exact number of pickles well then rounding will actually be a very useful tool but let's just focus on what it means to round to the nearest 10 so when they're talking about rounding to the nearest 10 we're going to be thinking about the tens place of the number so we can see right over here in our tens place we have a three and so that three represents three tens so the number 37 it's three tens and 7 ones so it is more than three tens and it's going to be less than four tens so this number is going to be more than three tens I could do it like this it's going to be more than three tenths which we can represent like that three tens is your ones or you might know that as 30 and it's going to be less than four tens or also known as 40 and so when you're rounding you're either going to round to the number of tens that is right below this number or the number of tens that is right above that but how do we know whether 37 rounded to the nearest 10 is going to be 30 or 40 well to answer that question let's first just do it visually on a number line and then we can come up with some rules for ourselves and so first of all let's just count by tens and to make sure we include 30 and 40 so if we start at 0 10 20 actually let me have a little bit more space because I want to see the interesting things that are going to go on 0 10 20 30 40 that's enough but I could just go to 50 just to complete this number line and so where is 37 on this number line well it's between 30 and 40 and if I wanted to make it a little bit clearer if I said that this is 35 right over there right in between 30 and 40 then 37 is going to be right about right about here so that is 37 and so when you're rounding to the nearest 10 and remember we're picking between three tens and four tens you say which 10 is it closest to is it closer to three tens or is it closer to four tens well you can just look at this and say hey it looks a lot closer to four tens and so in this situation 37 rounded to the nearest 10 is going to be 40 and so you might ask a question well give me another number what if someone said 32 rounded to the nearest ten well 32 is going to be right over here and then you'd say all right well that's between three tens and four tens but it's a lot closer to three tens so 32 rounded to the nearest ten is going to be is going to be 30 now an interesting question that you might be wondering is what if you're right in between what if we wanted around 35 to the nearest 10 35 once again it's between three tens and four tens between 30 and 40 which one do we round to if we want to round to the nearest ten well the rule is and this is really just something that the society has decided on is that if you're right in the middle you round up so the number 35 is going to round up to 40 even though it's exactly five away from each of these numbers 35 if you're right in between is going to round up to 40 if you're a little bit less than 35 then you're going to ground down to 30 but with that out of the way let's do some more examples let's do actually let's do an example of a three-digit number we're we're rounding to the nearest tenth let's say that we want to round the number 124 to the nearest ten well you could there's a couple of ways that you could think about this you could say that this is one hundred two tens and four ones or you could even view this as twelve tens and four ones so you could say hey this is in between twelve twelve tens and four ones it's greater than twelve tens which is a hundred and twenty and it's less than thirteen tens which is one hundred and thirty these are the two tens that are closest to this number and then to decide which one it rounds to you might already be able to think about it based on some of the rules we came up with but let me draw it on a number line for you so let me draw a number line and I'm not going to start at zero because we ought we have to get all the way to a hundred and thirty so let's just start I'll start at a hundred so this is one hundred one hundred and ten let me draw the number line we're going to have one hundred and twenty then we go to one hundred and thirty I'll just do one hundred forty here just for filling out the number line that I've drawn so far and then I'll draw the halfway mark which is 125 and then see it's halfway it's maybe a little bit closer to there and then 124 let me do it in this red color 124 is right over there 124 and so for trying to pick between 120 and 130 between twelve tens and thirteen tens which one is it closer to well we can see it's only four away from 120 while it's six away from 130 so we would round down we're going to round down to a hundred and twenty in this situation if we're rounding to the nearest ten if this was 125 or 126 127 our 28th 129 well then we would round to 130 and of course if it was 130 we would round it to 130 let's do one more example and actually I'm going to do a one digit number let's say we want around seven to the nearest ten I'll write it out around seven to the nearest nearest ten pause this video and see if you can do that all right well seven is between what two tens well seven is less than 110 so it's less than 110 and it's greater than zero tens so it's between zero tens which is just zero and one 10 which is 10 but which one does it round to well here once again we can draw our number line so we'll do zero and then this is 5 and then this is 10 and 7 is right about there that is where 7 is and we can either visually see that 7 is closer to 10 than it is to 0 it's only 3 away from 10 while it's 7 away from 0 so you would round up to 10 or you can use the rule that we just thought about 7 is greater than or equal to 5 so you round up you round to the 10 that is higher than this number if this number was if in the ones place I can say if your ones place is between 0 it's greater than or equal to 0 but less than 5 then you round down and you can see that happens in all of these situations if you looked at 37 you look at the ones place and your ones place here is greater than or equal to 5 so you round up here if your ones place it's greater than or equal to 5 it's 5 exactly in that situation so it's equal to 5 once again you round up if your ones place is less than 5 well in this situation we round down if your ones place is less than 5 you round down your ones place and here you only have a ones place but it's greater than or equal to 5 we rounded up