Math Antics - Measuring Distance - Free Educational videos for Students in K-12

Math Antics - Measuring Distance - By Mathantics

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00:03	Uh huh . Hi , I'm rob . Welcome to
00:07	Math Antics . In a previous video , we learned
00:10	about the most common units for measuring distances . In
00:13	this video , we're going to talk about how you
00:15	actually use some of those units when making a measurement
00:17	. In real life . Making measurements is something you
00:20	would typically learn how to do in science class .
00:22	But since measurement uses math to get the job done
00:25	, it's often taught math class too . So here
00:28	we go I suppose were given an object like this
00:31	pencil and were asked to measure its length in centimeters
00:34	to do that . We need some method or device
00:37	that will tell us how many centimeters long the pencil
00:39	is remembering that a centimeter is roughly the width of
00:43	a pinky finger . I could just use my finger
00:46	as that device and see how many finger wits it
00:48	takes to get from one end of the pencil to
00:50	the other . But something a little more accurate would
00:53	be nice and that's where a ruler comes in handy
00:57	. I , the great king robb ruler of all
01:00	the land , declare that the span of my royal
01:03	hand shall henceforth be the measure of all things in
01:07	my kingdom , great or small . Uh not that
01:11	kind of a ruler in math and science . A
01:14	ruler is a flat piece of material that has markings
01:17	on it that correspond to standard units of distance .
01:20	For example , this ruler has a series of markings
01:23	that correspond two on one side and cm on the
01:26	other . That's cool . We'll just ignore the inches
01:29	side and use a centimeter site for this measurement .
01:31	We start by moving the ruler so that the zero
01:34	centimeter mark is aligned as closely as we can with
01:37	one end of our pencil . Then we'll see where
01:40	the other end of the pencil lies on the scale
01:42	of centimeters . Looking at the numbers , you can
01:44	see that the other end lines up nicely with the
01:46	19 centimeter mark . So this pencil is 19 centimeters
01:50	long . But what if the pencil get sharpened and
01:53	then used and sharpened , then used again so that
01:56	it gets shorter . Now if we re measure it
01:58	with our ruler , you'll see that we have a
02:00	small problem . The tip of the pencil doesn't line
02:03	up with any of the centimeter marks anymore . It
02:05	lies somewhere between the 17 and 18 centimeter marks .
02:09	We could just say that it's between 17 and 18
02:11	cm long . But it would be nice if we
02:13	could be a little more accurate than that . Being
02:16	more accurate means making a measurement that is closer to
02:19	the true value . Fortunately , most rulers divide the
02:23	space between each centimeter mark into 10 equal parts that
02:26	represent mm , which are exactly 1/10 of a centimeter
02:30	. Because the millimeter marks are so much smaller ,
02:33	they don't have numbers on them . But if you
02:35	look closely you'll be able to count that there are
02:37	nine smaller lines that divide the centimeter into 10 equal
02:41	parts . The middle of these nine lines is usually
02:43	a little longer than the rest , so that it's
02:45	easier to tell where the halfway point is . Using
02:48	these subdivision marks , we can get a more accurate
02:51	measurement of the length of our sharpened pencil . Do
02:53	you see how the pencils tip ? Almost lines up
02:56	with the third subdivision line . That comes right after
02:58	the 17 centimeter mark . That means that the length
03:01	of the pencil is 17 cm plus three or 17.3
03:06	cm . Well that's a pretty close measurement . But
03:10	remember the tip of the pencil didn't line up exactly
03:12	with the third subdivision line , it went just a
03:14	little bit past it . Our ruler doesn't have marking
03:18	smaller than a millimeter . So it will be hard
03:20	for us to make a measurement more accurate than that
03:23	. But we could make an estimate for example ,
03:26	it looks like the pencil tip goes past the three
03:28	millimeter mark by a very small amount , maybe just
03:31	1/10 of a millimeter . So we could estimate that
03:34	its length is closer to 17.31 cm . If you
03:38	really did need a more accurate measurement , you need
03:41	to use a better measurement device that could provide that
03:43	level of accuracy . For example , calipers and micrometers
03:47	are devices that can measure distances as accurate as 1/10
03:50	or even 1/100 of a millimeter . And certain measurement
03:54	techniques using lasers can achieve even higher accuracies down to
03:57	extremely small units like nanometers . Those more advanced types
04:02	of measurements are beyond the scope of this video ,
04:04	but hopefully they'll help you realize something fundamental about the
04:07	nature of measurement . You can't measure the exact value
04:11	of something . There is always a limit to the
04:13	accuracy you can achieve based on your measurement device accuracy
04:17	is basically how close a measured value is to the
04:19	true value . And the measurement . The idea is
04:21	to get as close as possible or at least as
04:24	close as you need for your purposes . Luckily I
04:27	didn't really need to know the length of this pencil
04:29	down to the nearest 10th of a millimeter . In
04:31	fact , I didn't really need to know its length
04:33	at all since I'm just going to write with it
04:36	. Yeah , yeah . Yeah . Okay , now
04:40	that you understand what accuracy is and we've made a
04:43	measurement that was accurate to the nearest centimeter as well
04:46	as one that was accurate to the nearest millimeter .
04:48	Let's try making a measurement with the non metric side
04:50	of our ruler , which measures inches . Suppose we
04:54	want to know the length of this toothbrush and inches
04:57	to measure that we first line up one end of
04:59	the toothbrush with the start of the inches scale on
05:01	the ruler , which represents zero inches . Then we
05:04	see where the other end of the toothbrush lies on
05:06	that scale notice it's somewhere between seven and eight inches
05:10	. Can we get a more accurate measurement than that
05:13	? Yep , fortunately , as was the case with
05:15	centimeters on the other side of the ruler , inches
05:18	are usually subdivided into fractions of an inch . Also
05:21	on this particular ruler , each inch is subdivided into
05:25	eight equal parts . That means our toothbrush is not
05:28	quite as long as seven and 3/8 of an inch
05:30	, but it's a little longer than seven and 2/8
05:33	of an inch , which would be equivalent to seven
05:35	and one quarter inches . Whoa , whoa , whoa
05:38	! What are you talking about with all these fractions
05:40	? I thought this video was about measurement , not
05:42	fractions . Well , yes , but when things don't
05:46	line up exactly with the particular unit to get more
05:49	accuracy , you need to use fractions of that unit
05:52	. The metric system makes that look easy because things
05:55	are always divided by 10 . So the fractions match
05:57	up really nicely with our based in decimal system .
06:00	But English or American units have traditionally been divided up
06:04	differently . So the fractions you use for them are
06:07	a little bit trickier . So you're saying this is
06:09	all America's fault ? Well , America didn't invent the
06:13	system . It's just a traditional system of units that
06:16	goes way back in history to the days of monarchies
06:19	, so I guess it's probably some king's fault .
06:22	Yeah , how dare you . Anyway , it's true
06:26	that the traditional way of subdividing inches , it's kind
06:29	of messy when compared to the metric system . So
06:32	we'll help if we take a closer look basically there's
06:35	two ways that inches are commonly subdivided . One is
06:38	based on dividing by 10 and the other is based
06:41	on dividing by two . We'll start with the system
06:43	that's based on dividing by tin because that sounds a
06:46	lot like the metric system , doesn't it ? It
06:48	turns out that an inch can be divided up in
06:50	a metric like way even though an inch is not
06:53	a metric unit , here's how that works . You
06:56	start with an inch and then divided into 10 equal
06:58	parts . Each mark represents 1/10 of an inch .
07:01	So you can express the fractional parts easily with decimal
07:04	digits just like you do with the metric system .
07:07	For example , if a measurement came out to be
07:09	one and 2/10 inches , you just say it's 1.2
07:13	inches or if a measurement came out to be five
07:15	and 8/10 inches , you just say it's 5.8 inches
07:19	. And when you need more accuracy you can keep
07:22	subdividing by 10 so that you get hundreds of an
07:24	inch , 1000th of an inch , 10,000ths of an
07:27	inch and so on . This way of dividing up
07:30	inches is commonly used in american engineering , since it
07:33	has many of the benefits of the metric system even
07:35	though it's based on inches , the other way of
07:38	dividing up inches , which is still commonly used in
07:41	american construction is to divide them up by two .
07:44	Here's how that system works . You start with an
07:46	inch and then divide it into two equal parts .
07:49	That means you can now measure to an accuracy of
07:52	half an inch . Then you divide those half inches
07:54	by two . So we can measure to an accuracy
07:56	of a quarter of an inch . Then you divide
07:59	those quarter inches by two so you can measure to
08:02	an accuracy of an eighth of an inch and you
08:04	keep going like that divided by two . Again let
08:07	you measure to an accuracy of 1/16 of an inch
08:09	and divided by two . Again let you measure to
08:12	an accuracy of a 32nd of an inch . And
08:14	so on the basis of these fractional parts of an
08:17	inch are all different but they're all powers of two
08:20	. It's actually a really logical system if you think
08:23	about it but has the disadvantage that it's harder to
08:26	convert to decimal values when you need them . It's
08:28	also harder to add and subtract measurements if the fractions
08:31	don't have the same base When things are divided by
08:35	10 it's easy because we use decimal number places that
08:38	are specifically designed for counting fractions like tens , hundreds
08:42	and thousands but we don't have number of places for
08:45	halfs quarters and eighths Instead , it's very common for
08:48	people who use a lot of these traditional fractions of
08:51	an inch to just memorize some of the most common
08:53	equivalent decimal values and use a calculator to convert the
08:57	rest . For example , they might memorize things like
09:00	one half equals 0.51 quarter equals 0.25 and 1/8 equals
09:07	0.125 Now that you know the two main ways of
09:10	dividing up inches , let's go back to our toothbrush
09:12	example if we use a ruler that has divisions of
09:16	the 16th of an inch , you can see that
09:18	it's length is about seven and 5 16 7 inch
09:22	. That should be plenty accurate for brushing my teeth
09:26	. So now , you know the basics of how
09:28	you use a ruler to make measurements , but you
09:31	may need to brush up on your fractions to be
09:33	successful at it , see what I did there .
09:35	Last of all , I want to briefly introduce you
09:38	to some low tech devices that are commonly used to
09:40	measure longer distances . For example , a tape measure
09:44	is sort of a long , flexible ruler that can
09:46	be wound up on a spool to make it more
09:48	compact . It's a really handy device and carpenters use
09:52	them all the time when you unwind it . You
09:54	can measure much longer distances in the same way you
09:57	would with a ruler And it's a lot more convenient
10:00	than carrying around a 10 m stick . There's another
10:03	cool device often called a measuring wheel that can be
10:06	used to measure even longer distances by rolling a wheel
10:09	along the ground or any surface . It has a
10:12	counter on it that tallies up each foot or meter
10:14	that you roll it passed so you can measure the
10:16	total distance traveled . Of course , there are lots
10:19	of high tech methods for measuring distances nowadays too ,
10:23	and your phone can probably keep track of how many
10:25	miles you've traveled in a day and where you went
10:27	and who you talk to and what you might like
10:30	and might want to buy and and who you have
10:33	a crush on it . All right . That's the
10:37	basics of measuring distance . Remember the way to get
10:41	good at Math is to actually practice it . So
10:43	get on out there and start measuring stuff as always
10:47	. Thanks for watching Math Antics and I'll see you
10:49	next time you heard the man practice , learn more
10:54	at Math Antics dot com .

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