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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