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CCSS.Math:

let's now get some practice estimating multiplying with decimals so first year we have 7.8 times 307 is approximately equal to what when you see the squiggly equal sign that means approximately equal to 1 what so pause this video and see if you can figure out on your own alright so the way that I would think about doing it even if I was trying to do this in my head at the supermarket or something I'd say well okay this is I probably need paper to do this properly but gee seven point eight is awfully close to eight and 307 is pretty close to 300 so maybe I can estimate this by multiplying eight times 300 now this isn't going to be exact it's definitely going to be off but it's gonna give me a good sense of roughly what 7.8 times 307 is so what is 8 times 300 well 8 times 3 is 24 and so 8 times 300 would be 2400 we got these two more zeroes two more zeroes and so there you have it and luckily the people who wrote this question estimated in a very similar way to people when they estimate might not get the exact same answer but in this case we happen to let's do another example so here we're trying to estimate ninety-nine point eight seven times 19 so pause the video again and see if you can come up with the what a good estimation alright so once again not easy to do this in your head but this 99 and 87 hundredths is pretty close let me do this in a new color this is pretty close to 100 times and I could multiply a hundred times 19 that's actually not so difficult so for example I could say 100 times 19 is equal to 1900 but notice we don't see that choice here we could say look 1900 is definitely much closer to 2,000 than any of these other so that might be a good approximation now how did they get 2,000 well they rounded both of these numbers they said this is approximately 100 times 20 so it's not that it's not that it's the right thing to do to round this 19 up to 20 if you could do 100 times 19 this is actually gonna give you a slightly more accurate result than doing a hundred times 20 but 100 times 20 is even easier to estimate in your head but either way the closest choice here and that's why I guess these had to be multiple choice questions is mm let's do another example so here we are asked to multiply two point two one times five point one and we want to know what it approximately equals so once again we are estimating so pause this video and try to figure it out well we're just going to do the same thing we did in the last two examples two point two one and well first of all this is hard to do in my head and so two point two one well that's approximately if I round to the nearest two or to the nearest one I should say this is going to be two times five which is equal to ten so this would be approximately equal to ten and that is a choice now some of you might say well there's wet ways to get better estimations that you could still do with your head so for example you could say that this is pretty close to this is approximate let me do it over here this is approximately equal to two times five point one this is still pretty straightforward to do in your head this would be ten point two and so but you'd still say that this is by far the closest one or you could even say something like this is approximately equal to two point two times five what is this going to be equal to well two times five is ten and two tenths times five is another hole and so this is going to be equal to eleven so all of these might be things that you could estimate that you might be able to do in your head but the important thing to realize is however you do it by far ten is going to be the closest response to what you're getting at and ten would be a very natural estimation if you try to simplify both of these numbers when making that estimate