Math Antics - Rounding - Free Educational videos for Students in K-12

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00:03	Uh huh . Hi , welcome to Math Antics .
00:08	In this video , we're going to learn about an
00:09	important math concept called Rounding . To help you understand
00:14	what rounding is . Let's think about how numbers are
00:16	usually used most of the time numbers are used to
00:19	represent amounts of things like how many miles it is
00:22	to the supermarket or how many days until your birthday
00:25	or how many students went to your high school ?
00:28	How many students went to my high school ? Oh
00:31	about 2000 . Okay . But it wasn't exactly 2000
00:36	was it ? Well no , it was more like
00:38	1900 . Ah but it probably wasn't exactly 1900 either
00:44	, was it ? Well no , it was more
00:47	like 1860 . All Right Fine 1863 . See what
00:55	I did there at first the number used to represent
00:58	the students at high school was a round number .
01:00	It was a good estimate of how many students there
01:02	were , but it wasn't exact . The next two
01:05	numbers were a little closer to the truth , but
01:07	they were still estimates . Only the final number represented
01:10	the exact amount of students at the school . All
01:14	three of the estimates are rounded versions of the exact
01:17	count , but they have different levels of precision .
01:19	1860 was the most precise estimate , and 2000 was
01:24	the least precise estimate . So rounding a number basically
01:29	means making a less precise version of it . And
01:31	as you can see , there's usually multiple ways to
01:34	round a number depending on the level of precision that
01:36	you need . A really good way to understand what's
01:39	going on . When you round a number is to
01:41	look at a number line , here's 1,863 . If
01:46	we want to round it to the nearest 10 ,
01:48	we need to decide if it goes up to 1870
01:52	, or down to 1860 . But if we want
01:56	to round it to the nearest 100 , we need
01:58	to decide if it goes up to 1900 or down
02:02	to 1800 . And if we want to round it
02:05	to the nearest 1000 , we need to decide if
02:08	it goes up to 2000 or down to 1000 .
02:11	And in each case the decision was based on which
02:14	round number was closer to the original exact number ,
02:19	but you might be wondering why would we ever want
02:22	to make a number less precise in the first place
02:25	? What is rounding good for ? Well rounded numbers
02:29	can often make them a lot easier to do calculations
02:31	with . Like it would be a lot easier to
02:34	quickly add 305 100 Then it would be to add
02:38	312 and 498 . Or sometimes you just don't need
02:43	very much precision . Like you might not need to
02:46	know that your dog weighs 55.83297 kg 55.8 kg might
02:54	be precise enough . And some numbers like repeating decimals
02:58	or irrational numbers have to be rounded off because we
03:01	can't just keep writing decimal digits forever . Okay ,
03:05	now that you know what rounding is and why we
03:07	do it for the rest of this video , we're
03:09	going to focus on learning the procedure we follow to
03:12	round off a number . Do you remember how our
03:15	number system is based on digits and number of places
03:18	? Each digit of a number occupies a particular number
03:21	. Place in each number place is named according to
03:24	the amount it represents or counts . And it's important
03:28	to know those names whenever you're rounding a number Because
03:30	you'll usually be asked around to a specific number of
03:33	place . For example , you may be asked around
03:35	a number to the nearest 10 or the nearest 100
03:39	Or you might be asked around a number off to
03:41	the nearest 10th or 10th . You may even be
03:44	asked around to the nearest whole number , which is
03:46	another way of asking you to round to the ones
03:48	place . Okay , so when you're asked around a
03:51	number , the first step is to pay very close
03:54	attention to which number place you need to round two
03:57	. That number place is important because it represents the
03:59	smallest unit of counting that you're going to keep in
04:02	your rounded version of the number . In fact ,
04:05	that number of place and the digit inside it is
04:08	so important that I'm going to give it a special
04:10	name just for this video . Let's call it the
04:13	Target . As I mentioned , rounding a number means
04:16	making a new less precise version of it in that
04:20	new number , any digits that are a number of
04:22	places smaller than the Target will automatically get replaced with
04:26	zeros . And in most cases any digits that are
04:29	a number of places larger than the Target will automatically
04:32	be kept the same in the new rounded version .
04:35	There are some exceptions as we'll see later in this
04:37	video . So that seems pretty simple . All the
04:40	bigger digits you keep and all the smaller digits zero
04:43	. But what about that target digit itself ? What
04:46	do we do with that ? Well , we're going
04:48	to do one of two things . We're either going
04:50	to keep that digit the same or we're going to
04:53	increase it by one . If we keep that target
04:56	digit the same , that's called rounding down . Which
04:59	might seem strange at first . I mean how can
05:02	leaving the digit the same be rounding down ? But
05:05	remember we're going to automatically replace all of the smaller
05:09	places with zero . And doing that makes surrounded number
05:12	smaller . Even if the target digits stays the same
05:16	. On the other hand , increasing the target digit
05:19	by one is called rounding up since the new rounded
05:22	number will be larger than the original number . All
05:25	right . But how do we decide which to do
05:28	? How do we know if we keep the target
05:29	digit the same or increase it by one ? The
05:33	key is to look at the digit in the next
05:35	smaller number . Place the digit that's just to the
05:38	right of the target digit . If that digit is
05:41	less than five . In other words if it's a
05:43	0123 or four , then we'll leave the target digit
05:48	the same in the rounded version . But if the
05:51	digit is a five or greater 5678 or nine ,
05:56	then we'll increase the target digit by one . Okay
06:00	, so now that you know the basic procedure for
06:03	rounding numbers , let's try a few specific examples .
06:06	Here's the first one . Round 24623 to the nearest
06:12	100 . Since we need to round to the nearest
06:15	100 we first need to identify the digits in the
06:17	hundreds . Place that digit is a six so that's
06:21	our target and we know that any digits to the
06:23	right of the target will be replaced with zeros and
06:26	are rounded version . Next , let's decide what to
06:29	do with the target digit . We either keep it
06:32	the same or we increase it by one . To
06:35	decide , we look at the value of the next
06:37	digit to the right since that digit is only a
06:40	two which is less than five . We round down
06:43	which means that we'll keep the target digit the same
06:46	in the rounded number last we just keep all the
06:49	digits and bigger number places the same in the rounded
06:52	version There we've rounded the original number to the nearest
06:56	100 the answer is 24,600 . Let's try another problem
07:02	. This one has some decimal digits 32.725 and were
07:07	asked to round it to the nearest whole number .
07:09	That means our target digit is in the ones place
07:12	we need to round it to the nearest one .
07:15	So any digits to the right of the ones place
07:17	will just be replaced with zeros in the rounded version
07:21	. Now to decide what to do with the target
07:23	digit , we look at the next digit to the
07:25	right since that digit is a seven will round up
07:28	this time . That means we'll increase our target digit
07:31	by one and finally we keep any digits to the
07:35	left of the target digit the same in this case
07:38	, that's just the three . So we've rounded this
07:40	number off to 33.0 or just 33 . Since we
07:45	don't really need those extra zeros after the decimal point
07:48	Ready for one more let's round 65.7991 to the nearest
07:54	100th . The first step is to identify the hundreds
07:57	place as our target . That place contains the Digit
08:00	nine . All the digits in smaller number of places
08:03	will just be replaced with zero and the rounded version
08:07	. Next we need to decide if we leave the
08:09	target digit the same or increase it by one .
08:11	So we look at the digit to the right of
08:13	the target , it's A nine also so we'll definitely
08:16	be rounding up . But since the target digit is
08:19	already a nine , raising it by one is a
08:22	little more complicated . When you add one to a
08:25	digit that's already nine , you need to change it
08:27	to zero and increase the digit in the next bigger
08:30	number . Place by one . So that means that
08:33	our target digit will become zero and we need to
08:36	increase the digit in the next bigger number . Place
08:38	that digit is a seven so we'll increase it to
08:40	an eight . The rest of the digits in the
08:43	original number will be kept the same in the rounded
08:45	version . So are rounded version will be 65.80 .
08:50	As you can see in some cases rounding can actually
08:53	change the digits to the left of the target digit
08:55	. Also it's sort of a domino effect that can
08:58	happen when rounding numbers . Mhm . If you have
09:14	a lot of nines Rounding can bump them all up
09:17	like a chain reaction . Like what if you need
09:19	to round 1,999,999 to the nearest 10 . The nine
09:26	in the ones place tells us that we need to
09:28	round our target digit up by one but it's already
09:31	a nine . So we need to zero it and
09:33	increase the next number place but that's already a nine
09:36	. So we need to zero it and increase the
09:38	next number of place But that's already and I am
09:40	. And so the pattern continues until we end up
09:43	with two million as our final round their number .
09:46	So sometimes rounding a number is pretty simple and other
09:50	times it's a little more involved . The key is
09:53	to remember the rule that if the digit to the
09:55	right of the target is less than five , we
09:58	leave the target digit the same . But if it's
10:01	five or more we increase the target digit by one
10:05	. Even if that causes a chain reaction with the
10:07	bigger number . Places . All right . So now
10:10	, you know a lot about rounding numbers . You
10:12	know why we round numbers and you've seen the basic
10:15	procedure in action , but just watching a video about
10:18	rounding isn't enough to get really good at it .
10:21	The only way to do that is to practice .
10:23	So be sure to try rounding some numbers on your
10:25	own . In fact , rounding is such an important
10:28	mask , you'll that you should probably practice it a
10:30	lot until you've really got it mastered . As always
10:33	. Thanks for watching Math Antics and I'll see you
10:35	next time . Learn more at Math Antics dot com
00:0-1	.

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