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we're asked to round 150 to 137 245 and 354 to the nearest 100 which is another way of saying round each of these numbers to the nearest multiple of 100 so let's think about them one by one so let's draw a number line here and here I'm counting up by hundreds these what I've marked your hundred two hundred three hundred four hundred these are all multiples of 100 I could keep going up I could go to five hundred six hundred so on and so forth and let's start with 152 well where does 152 sit so it is halfway in between is 150 152 is going to be right to the right of that so that's 152 right over here so what are our two options we might round up the multiple of 100 above 152 is 200 the multiple of 100 below 152 is 100 so which direction do we go in do we round up to 200 or we around ground down to 100 well if we're rounding to the nearest hundred if we're rounding to the nearest hundred we want to look at one place to the right of that we want to look at the tens place to decide which multiple of 100 is closer to and the rules are very similar to when we're round rounding to the nearest tens place or really any place we look one place to the right of it so in this case we look at the tens place and we say if this is 5 or larger we round up and this is 5 or larger so we're going to round up to 200 so this we're going to round 152 we're going to round to 200 which also makes sense 152 is a little bit closer to 200 it's 48 away from 200 than it is to 100 it's 52 away from 100 so it makes sense to go up it will go up to the nearest multiple of 100 now let's think about 137 137 and I encourage you to now pause the video and try to round each of these other three numbers to the nearest hundred well 137 is going to sit someplace going to sit right over here 137 is going to be right over there so two options we can round down to 100 that's the mole of 100 below 137 or we could round up we could round up to 200 well 137 just looking at it is clearly closer to 100 or we could apply our rule if we're if we're rounding to the nearest hundred we want to look at one place to the right of that we want to look at the tens place if this is five or larger we round up if it's less than 5 we round down so in this case we would round down to 100 let's do the same thing with 245 if you haven't pause it and try it yourself once again I want to emphasize that'll make it really valuable for you to try it on your own so let's plot where 245 is so 245 is right around this is 250 so 245 might be right around here so 245 and let's apply that rule if we're trying to round to the nearest hundred we would look to one place to the right we'll look at the tens place we can ignore the ones place we look at the tens place here if it is greater than or equal to 5 we round up if it is less than 5 we round down so here we're clearly going to round down and when we round down we're going to round down to the multiple of 100 that's below that's directly below 245 well that's going to be we're going to round down to 200 we had two options if we rounded up we've gone to 300 if we rounded down we would go to 200 we're clearly closer to 200 and we can verify that with the rule the tens place were in the 40s here the tens places of four we're going to round down now let's think about 354 354 if we were to plot that this is 350 354 might be right over here 354 so if we round it down we would go to 300 if we round it up we'd go to 400 now let's apply a rule and let's also think about it on the number line this is all about finding the multiple of 100 that is closest to if you're trying to round to the nearest hundred you want it so you're on around to the nearest hundred you want to look at the tens place a place to the right of what of the place you're rounding to if the tens place is a five or larger you're going to round up this is a five are larger so we're going to round up we're going to round up to we're going to round up to 400 and that also makes sense the rule is really valuable if you're right at 350 right in between then you would need the rule to say hey let's look at this five and round up but 354 is also closer to 400 than it is to 300 it's 54 away from 300 it's 46 away from 400 so it makes sense that we would round up to 400