Math Antics - Units of Distance - Free Educational videos for Students in K-12 | Lumos Learning

Math Antics - Units of Distance - Free Educational videos for Students in k-12


Math Antics - Units of Distance - By Mathantics



Transcript
00:03 Uh huh . Hi , I'm rob . Welcome to
00:07 Math Antics . In our previous video , we learned
00:10 the basic idea behind measurement and the metric system .
00:13 In this video , we're going to focus on some
00:14 common units of distance to help you develop an intuition
00:17 about their sizes and what sorts of things they're used
00:20 to measure . As you probably know , distance is
00:23 a one dimensional quantity that describes how far it is
00:26 between two points . Several different words are used as
00:29 synonyms for distance , such as length , height ,
00:32 width or depth . And the word you use usually
00:35 depends on how an object is positioned relative to you
00:38 . For example , if you're measuring a distance from
00:41 side to side , you might call it a width
00:43 . But if you're measuring the distance up and down
00:46 , you'll probably call it height . But no matter
00:48 which word you use for distance , the same kind
00:50 of unit supply . But as we learned in the
00:52 last video , there's many different units of distance that
00:55 we could use , such as meters kilometers or millimeters
00:59 . And there are several other non metric units of
01:01 distance , like feet or inches , that we could
01:03 use to . But why have different sized units at
01:06 all ? I mean , wouldn't it be much simpler
01:08 if we just picked one unit of distance and always
01:10 use that one ? Well , we could . But
01:13 the main reason we have different units to choose from
01:16 is that there's a huge variety in the size of
01:19 objects that we might want to measure . Some are
01:21 really , really big , while others are so incredibly
01:24 small that you can't even see them . This wide
01:27 range of possible sizes is called the relative scale of
01:31 objects . And it's helpful to choose a unit of
01:34 measurement that's a good match for a particular object scale
01:37 . Here's what I mean by that , suppose I
01:39 decided to measure my height using mm , which are
01:42 really small units about the size of an ant .
01:45 I would be about 1980 tall . And while that's
01:50 a correct measurement , it's kind of a big number
01:53 that makes me seem even taller than I really am
01:55 . On the other hand , if I decided to
01:57 measure my height using a really big unit like km
02:00 , I'd be a mere 0.00198 km tall . Again
02:06 , that's a correct measurement , but it's a really
02:08 small number that makes me seem tiny . But what
02:11 if I choose a unit that's somewhere in between like
02:14 plain old meters ? A meter is as long as
02:17 this stick , which is why I like to call
02:19 it a meter stick . And if I use it
02:21 to measure my height , I'd be 198 m tall
02:27 , which is just a hair shy of two m
02:29 . So it would be fair to say that I'm
02:31 about two m tall , which is a nice easy
02:34 number to work with . See the advantage of having
02:36 different sized units for measuring distances . You can choose
02:39 a unit that's relatively close to the scale of the
02:42 thing that you want to measure so that the numbers
02:44 you get are more relatable and easy to work with
02:47 . But that means that you need to know about
02:49 the different units of distance so you can make a
02:51 good choice . Right ? So that's what we're going
02:53 to focus on in the rest of this video .
02:55 Specifically , we're going to learn about four traditional units
02:58 that are still used in America for measuring distances inches
03:01 , feet , yards and miles . And then we'll
03:04 see how those compared to the four most popular metric
03:06 units for measuring distance millimeters centimeters meters and kilometers .
03:11 Let's start with an inch . An inch is about
03:14 this wide , which is pretty close to the width
03:16 of a human eye or perhaps the width of your
03:18 thumb if you have big fingers . An inch is
03:21 a good sized unit for measuring objects that we commonly
03:23 interact with . For example , a ping pong ball
03:26 is about 1.5 inches in diameter And my phone is
03:30 about six tall and an un sharpened pencil is about
03:33 eight long and it's common to measure things that are
03:37 smaller than an inch . Using fractions like a half
03:40 inch or accord french , we'll learn more about fractions
03:43 of an inch in a future video when we talk
03:45 about measuring devices like rulers and tape measures . Okay
03:49 , But what if we want to measure things much
03:51 bigger than an inch ? Like a car ? Well
03:53 , we could still use inches and just end up
03:55 with a big measurement or we can use a bigger
03:58 unit called the foot . A foot is exactly the
04:02 same distance as 12 stacked into end . So it's
04:05 about this long . Some familiar objects that are approximately
04:10 a foot long are well your foot . For one
04:12 thing , of course , different people have different sites
04:15 , feet and most people have feet that are less
04:17 than a foot long , but the length of the
04:19 average shoe is a pretty good estimate for a foot
04:23 . Mhm . And that's why you'll sometimes see people
04:26 walking off a distance , heel to toe to estimate
04:29 how many feet that distances . Other things that are
04:32 about a foot long are a foot long sub sandwich
04:35 , a tall water bottle or a three ring binder
04:38 , and a foot is a convenient unit for measuring
04:40 things like a person's height . I happen to be
04:43 6.5 ft tall , or the width of a desk
04:46 minds about five ft wide , or the length of
04:49 the car , minds about 15 ft long . All
04:52 right . But what if you want to measure something
04:54 much bigger than a foot , like an athletic field
04:57 ? Well , that's what a yard is for .
04:59 A yard is an english unit of measurement . That's
05:02 exactly the same as three ft placed end to end
05:05 . So a yard is about this long . In
05:08 general , yards aren't used as often as feet .
05:11 But one place where yards are used all the time
05:13 is an American football between the end zones . An
05:16 American football field is 100 yards long and those 100
05:20 yards are divided into subgroups of five yards each .
05:23 So you can measure some pretty big distances with feet
05:26 in yards . But what if you need a unit
05:28 that's even bigger ? Well , that's where miles come
05:31 in handy . A mile is equivalent to 1760 yards
05:36 . That's the distance you would get if you put
05:38 17.6 football fields end to end , which is pretty
05:41 far . A mile is much bigger than the other
05:45 three units we've looked at so far . If this
05:47 is an inch then this is a foot and this
05:50 is a yard , then this is a mile .
05:53 Because miles are so long . They're mainly used to
05:56 measure distances between various places on earth and how far
06:00 people travel . For example , the distance from new
06:03 york city to Washington , D . C . Is
06:05 roughly 200 miles as the crow flies . And the
06:08 distance from the east coast of the US to the
06:10 West Coast or the best coast , whichever you like
06:13 to call it , is over 2600 miles . Sure
06:17 , you could use miles to measure smaller distances ,
06:20 but it would be a little silly to tell your
06:22 friend that your 0.994 miles tall . But go ahead
06:27 if you want to . Okay , so that takes
06:30 care of the four main traditional units . Now let's
06:32 have a look at the four most common metric or
06:34 S . I . Units of distance which are preferred
06:36 by the scientific community . And most countries , we're
06:39 gonna start with the unit called a centimeter . A
06:42 centimeter is pretty small . It's approximately the width of
06:45 your pinky finger or the diameter Of a small marble
06:49 . If you compare a centimeter to an inch ,
06:51 you'll find that it takes about 2.5 cm to equal
06:54 1 2.54 cm to be exact . So centimeters are
06:59 also really good units for measuring objects that you commonly
07:02 interact with . This rechargeable battery is about five centimeters
07:05 long . This tennis ball is about 6.5 centimeters in
07:09 diameter , and this flashlight is nearly 23 centimeters long
07:13 . Whoa . But what if you want to measure
07:14 things that are smaller than a centimeter ? Well millimeters
07:18 might be a good choice . A millimeter is exactly
07:20 1/10 of the centimeter . That means if you took
07:23 a centimeter and divided it up into 10 equal parts
07:26 , each of those parts would be the distance of
07:28 one millimeter . A millimeter is about the width of
07:32 a small black ant . So millimeters are good for
07:34 measuring small things like the width of a sunflower seed
07:37 or the thickness of a smartphone . Okay , but
07:41 what if we need to measure something bigger than a
07:42 centimeter ? No problem . We can just use meters
07:45 . A meter is a unit of distance that's about
07:48 this long that looks similar in length to a yard
07:51 , doesn't it ? It turns out that a meter
07:53 is just a little longer than a yard , approximately
07:56 10 longer . But the important thing to know about
07:59 a meter Is that it's the exact distance you'd get
08:02 if you took 100 cm and place them into end
08:05 , yep , 100 centimeters equals one m , which
08:09 means that a centimeter is 1 1/100 of a meter
08:12 , m are great for measuring distances like the height
08:15 of the building . This one is 381 m tall
08:19 . Or the distance around a racetrack , which is
08:21 400 m . But if you needed to measure even
08:24 longer distances , you could use kilometers or kilometers .
08:28 A kilometer is the distance you'd get if you took
08:30 exactly 1000 m and place them into end . That's
08:34 a long distance . It's much longer than the other
08:37 metric units . We've seen . If this is a
08:39 millimeter , this is a centimeter and this is a
08:42 meter , then this is a kilometer as you can
08:45 see . A kilometer is in the same scale range
08:48 as a mile , but a mile is even longer
08:50 than a kilometer . In fact , it takes just
08:53 a bit more than 1.6 km to be the same
08:55 distance as a mile . And because they're big like
08:58 miles , kilometers are also primarily used to measure distances
09:01 between different locations on the earth or even in space
09:05 . For example , it's about 4000 km from the
09:08 east coast of Australia to the West Coast , and
09:11 it's approximately 384,000 km from the Earth to the Moon
09:16 . Okay , so now that you have a better
09:18 idea about the size of the most common traditional and
09:21 metric units of distance , let's do some side by
09:23 side comparisons . So you get a better feel for
09:25 how these units relate to each other again . Let's
09:28 start with an inch . We already learned that an
09:31 inch is the same distance as 2.54 centimeters . Right
09:35 , So how many millimeters would be equal to an
09:37 inch ? Well , since there's exactly 10 in each
09:41 centimeter , all we have to do is multiply 2.54
09:45 by 10 . And we see that there are 25.4
09:47 mm in an inch . But now let's bring in
09:50 a foot . We know that there's exactly 12 in
09:53 a foot , which means that a foot is 12
09:56 times longer than an inch . So how many cm
09:59 are there in a foot ? Well , since there's
10:01 2.54 cm in an inch , if we multiply that
10:05 by 12 we'll know how many cm are in a
10:07 foot . Using my trusty calculator , 2.54 times 12
10:12 equals 30.48 . So a foot is exactly 30.48 cm
10:17 long . Those are exact conversions between inches , centimeters
10:21 and feet . But what if you only need estimates
10:24 or close enough measurements in that case ? Just remember
10:27 that an inch is about 2.5 centimeters and a foot
10:31 is about 30 centimeters . Let's do another quick comparison
10:34 . Starting with 10 centimetres Instead . If you have
10:37 10 centimetres , it's easy to see that it's equivalent
10:40 to 100 millimeters Since there's 10 in every centimeter ,
10:44 10 times 10 equals 100 . But what would that
10:47 same distance be in inches ? Well , an inch
10:50 is bigger than a centimeter And it takes approximately 2.5
10:54 cm to equal an inch . Right ? So if
10:57 we divide the 10 centimetres up into groups of 2.5
11:01 , which is the same as dividing 10 by 2.5
11:04 , it forms four equal sized groups . That means
11:07 10 cm is very close to being the same as
11:10 4" . The reason it's only very close is because
11:14 we use the estimate 2.5 cm per inch instead of
11:17 the exact value of 2.54 . If we divided 10
11:21 by 2.54 instead we would see that 10 centimeters is
11:25 more like 3.937 inches . But for is a great
11:28 estimate and it's easier to remember . 10 cm is
11:32 about 4" . Now that we've compared some of the
11:35 smaller units , let's briefly look at the bigger ones
11:38 . We learned that a meter is about 10 bigger
11:41 than a yard Or roughly 1.1 yards . That's a
11:44 good estimate . But more precisely to three decimal places
11:48 . A meter is 1.094 yards . A yard is
11:52 three ft . So that means a meter is a
11:54 little more than three ft . How much more ?
11:57 Well , each foot in the yard is 12" ,
12:00 so a yard is 36 since three times 12 equals
12:04 36 . Our estimate is that a meter is 10
12:07 bigger than a yard , So what's 10% of 36
12:11 inches , yep . 3.6 inches . And if we
12:14 add that to 36 inches , that means a meter
12:17 is pretty close to 39.6 inches or 40 inches .
12:21 If we round up a little And that checks out
12:24 because remember , we just estimated that 10 cm is
12:27 about 4" . Well , a meter is 10 times
12:30 as long as 10 cm And 40 is 10 times
12:34 as long as 4" . So , a good rough
12:37 estimate of A meter is that it's about 40 long
12:41 . Last of all , let's compare a kilometer to
12:43 a mile . A mile is longer than a kilometer
12:47 . In fact , it takes approximately 1.6 km to
12:50 equal one mile . The exact value is 1.609344 .
12:56 That means that a kilometer is only about 62 of
12:59 the distance of a mile . A good way to
13:01 remember the estimated difference between a mile and kilometer is
13:05 to multiply both by 10 and remember that 10 miles
13:08 is roughly the same distance as 16 km . That
13:11 fun fact may come in handy on your next road
13:13 trip . Oh , we should be at the campsite
13:16 in 16 km . 16 km . We're never going
13:20 to get there . Oh , chill back there .
13:22 That's only 10 miles . Yes . All right .
13:26 So that's a basic overview of the most common units
13:29 used to measure distance . Hopefully it's given you a
13:32 better idea of how big each unit is , how
13:35 the various units relate to each other and what sorts
13:38 of objects they're helpful for measuring . Again , there
13:41 aren't too many exercises for this section , but doing
13:43 them will help you remember the relationships between some of
13:46 these important units . As always . Thanks for watching
13:49 Math Antics and I'll see you next time learn more
13:53 at Math Antics dot com .
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