Hi I’m Rob, welcome to Math Antics!
In our previous video, we learned the basic idea behind measurement and the Metric System.
In this video we’re gonna focus on some common units of distance
to help you develop an intuition about their sizes
and what sorts of things they’re used to measure.
As you probably know, distance is a 1-dimensional quantity
that describes how far it is between two points.
Several different words are used as synonyms for distances,
such as “length”, “height”, “width” or “depth”.
And the word you use usually depends on how an object is positioned relative to you.
For example, if you’re measuring a distance from side to side,
you might call it a “width”,
but if you’re measuring a distance up and down,
you’ll probably call it “height”.
But no matter which word you use for distance, the same kind of units apply.
But as we learned in the last video,
there’s many different units of distance that we could use,
such as meters, kilometers or millimeters.
And there are several other non-metric units of distance
like feet or inches that we could use too.
But why have different size units at all?
I mean… Wouldn’t it be much simpler if we just
picked one unit of distance and always used that one?
Well, we could… but the main reason we have different units to choose from
is that there’s a huge variety in the size of objects that we might want to measure.
Some are really, really big,
while others are so incredibly small that you can’t even see them.
This wide ranges of possible sizes is called the relative scale of objects,
and it’s helpful to chose a unit of measurement that’s a good match for a particular object’s scale.
Here’s what I mean by that…
Suppose I decide to measure my height using millimeters,
which are really small units about the size of an ant.
I would be about 1,980 millimeters tall!
And while that’s a correct measurement,
it’s kind of a big number that makes me seem even taller than I really am.
On the other hand,
if I decide to measure my height using a really big unit like kilometers
I’d be a mere 0.00198 kilometers tall.
Again, that’s a correct measurement,
but it’s a really small number that makes me seem tiny!
But what if I choose a unit that’s somewhere in-between, like plain ol’ meters?
A meter is as long as this stick, which is why I like to call it a “meter stick”.
And If I use it to measure my height, I’d be 1.98 meters tall, which just a hair shy of 2 meters.
So it would be fair to say that I’m about 2 meters tall
which is a nice easy number to work with.
See the advantage of having different sized units for measuring distances?
You can choose a unit that’s relatively close to the scale of the thing that you want to measure
so that the numbers you get are more relatable and easy to work with.
But that means that you need to know about the different units of distance
so you can make a good choice, right?
So that’s what we’re going to focus on in the rest of this video.
Specifically, we’re gonna learn about 4 traditional units
that are still used in America for measuring distances:
inches, feet, yards and miles.
And then we’ll see how those compare to the four most popular Metric units for measuring distance:
millimeters, centimeters, meters, and kilometers.
Let’s start with an inch.
An inch is about this wide,
which is pretty close to the width of a human eye
or perhaps the width of your thumb if you have big fingers.
An inch is a good size unit for measuring objects that we commonly interact with.
For example, a ping-pong ball is about one and a half inches in diameter,
and my phone is about 6 inches tall,
and an unsharpened pencil is about 8 inches long.
And it’s common to measure things that are smaller than an inch,
using fractions like, a half-inch or a quarter-inch.
We’ll learn more about fractions of an inch in a future video
when we talk about measuring devices like rulers and tape measures.
Okay, but what if we want to measure things much bigger than an inch… like a car?
Well, we could still use inches and just end up with a big measurement.
Or, we can use a bigger unit called a “foot”.
A foot is exactly the same distance as 12 inches stacked end-to-end.
So it’s about this long…
Some familiar objects that are approximately a foot long are…
well… your foot for one thing.
Of course, different people have different sized feet,
and most people have feet that are less than a foot long,
but the length of the average shoe is a pretty good estimate of a foot.
And that’s why you’ll sometimes see people walking off a distance heel-to-toe
to estimate how many feet that distance is.
Other things that are about a foot long are:
a foot long sub sandwich,
a tall water bottle,
or a three ring-binder.
And a foot is a convenient unit for measuring things like a person’s height…
I happen to be six and a half feet tall.
Or the width of a desk…
mine’s about 5 feet wide.
Or the length of a car…
mine’s about 15 feet long.
Alright, but what if you want to measure something much bigger than a foot…
like an athletic field?
Well, that’s what a “yard” is for.
A yard is an English unit of measurement that’s exactly the same as 3 feet placed end-to-end.
So a yard is about this long.
In general, yards aren’t used as often as feet,
but one place where yards are used all the time is in American Football.
Between the end-zones, an American football field is 100 yards long.
And those 100 yards are divided into sub-groups of 5 yards each.
So you can measure some pretty big distances with feet and yards,
but what if you need a unit that’s even bigger?
Well, that’s where miles come in handy.
A mile is equivalent to 1,760 yards.
That’s the distance you’d get if you put 17.6 football fields end-to-end, which is pretty far.
A mile is much bigger than the other three units we’ve looked at so far.
If this is an inch,
then this is a foot
and this is a yard…
then this is a mile!
Because miles are so long, they’re mainly used to measure distances
between various places on Earth and how far people travel.
For example, the distance from New York City to Washington DC
is roughly 200 miles (as the crow flies).
And the distance from the east coast of the U.S. to the west coat
(or the best coast, whichever you like to call it) is over 2,600 miles!
Sure, you could use miles to measure smaller distances,
but it’d be a little silly to tell your friend that you're 0.000994 miles tall.
But go ahead if you want to.
Okay, so that takes care of the four main ‘traditional’ units…
now let’s have a look at the four most common Metric (or SI) Units of distance,
which are preferred by the scientific community and most countries.
We’re gonna start with a unit called a centimeter.
A centimeter is pretty small… it’s approximately the width of your pinky finger
or the diameter …of a small marble.
If you compare a centimeter to an inch, you’ll find that
it takes about two and a half centimeters to equal one inch (2.54 centimeters to be exact).
So centimeters are also really good units
for measuring objects that you commonly interact with.
This rechargeable battery is about 5 cm long,
this tennis ball is about 6.5 cm in diameter,
and this flashlight is nearly 23 cm long.
But what if you want to measure things that are smaller than a centimeter?
Well… millimeters might be a good choice.
A millimeter is exactly one-tenth of a centimeter.
That means, if you took a centimeter and divided it up into 10 equal parts,
each of those parts would be the distance of one millimeter.
A millimeter is about the width of a small black ant,
so millimeters are good for measuring small things
like the width of a sunflower seed,
or the thickness of a smart phone.
Okay, but what if we need to measure something bigger than a centimeter?
No problem, we can just use meters.
A meter is a unit of distance that’s about this long…
That looks like a similar length to a yard, doesn’t it?
It turns out that a meter is just a little longer than a yard. …approximately 10% longer.
But the important thing to know about a meter is that
it’s the exact distance you’d get if you took 100 centimeters and placed them end-to-end.
Yep, 100 centimeters equals 1 meter which means that a centimeter is one 100th of a meter.
Meters are great for measuring distances like the height of a building.
This one is 381 meters tall.
…or the distance around a race track, which is 400 meters.
But if you needed to measure even longer distances, you could use kilometers.
A kilometer is the distance you’d get if you took exactly 1,000 meters and placed them end-to-end.
That’s a long distance.
It’s much longer than the other metric units we’ve seen.
If this is a millimeter,
this is a centimeter,
and this is a meter
…then this is a kilometer!
As you can see, a kilometer is in the same scale range as a mile…
but a mile is even longer that a kilometer.
In fact, it takes just a bit more than 1.6 kilometers to be the same distance as a mile.
And because they’re big like miles, kilometers are also primarily used
to measure distances between different locations on the earth, or even in space!
For example, it’s about 4,000 km from the east coast of Australia to the west coast,
and it’s approximately 384,000 km from the earth to the moon!
Okay, so now that you have a better idea about the size
of the most common traditional and metric units of distance,
let’s do some side-by-side comparisons so you get a better feel for how these units relate to each other.
Again, let’s start with an inch.
We already learned that an inch is the same distance as 2.54 centimeters, right?
So, how many millimeters would be equal to an inch?
Well, since there are exactly 10 millimeters in each centimeter,
all we have to do is multiply 2.54 by 10 and we see that there are 25.4 millimeters in an inch!
But now let’s bring in a foot.
We know that there are exactly 12 inches in a foot,
which means a foot is 12 times longer than an inch.
So… how many centimeters are there in a foot?
Well, since there are 2.54 cm in an inch,
if we multiply that by 12, we’ll know how many centimeters are in a foot.
Using my trusty calculator: 2.54 x 12 = 30.48,
So a foot is exactly 30.48 cm long.
Those are exact conversion between inches, centimeters and feet,
but what if you only need estimates, or close enough measurements?
In that case, just remember that an inch is about 2.5 cm and a foot is about 30 cm.
Let’s do another quick comparison starting with 10 centimeters instead.
If you have 10 centimeters, it’s easy to see that it’s equivalent to 100 millimeters
since there are 10 millimeters in every centimeter (10 x 10 = 100)
But what would that same distance be in inches?
Well, an inch is bigger than a centimeter,
and it takes approximately 2.5 centimeters to equal 1 inch, right?
So if we divide the 10 centimeters up into groups of 2.5 (which is the same as dividing 10 by 2.5)
it forms 4 equal sized groups.
That means 10 centimeters is very close to being the same as 4 inches.
The reason it’s only very close is because we used the estimate of 2.5 cm per inch
instead of the exact value of 2.54.
If we divided 10 by 2.54 instead, we’d see that 10 cm is more like 3.937 inches.
But 4 is a great estimate and it's easier to remember.
10 cm is about 4 inches.
Now that we’ve compared some of the smaller units, let’s briefly look at the bigger ones.
We learned that a meter is about 10% bigger than a yard, or roughly 1.1 yards.
That’s a good estimate, but more precisely (to 3 decimal places), a meter is 1.094 yards.
A yard is 3 feet, so that means a meter is a little more than 3 feet.
How much more?
Well, each foot in a yard is 12 inches,
so a yard is 36 inches (since 3 x 12 = 36).
Our estimate is that a meter is 10% bigger than a yard,
so what’s 10% of 36 inches?
Yep… 3.6 inches.
And if we add that to 36 inches that means a meter is pretty close to 39.6 inches
(or 40 inches if we round up a little).
And that checks out because remember that we just estimated that 10 cm is about 4 inches.
Well, a meter is ten times as long as 10 cm,
and 40 inches is ten times as long as 4 inches,
so a good rough estimate of a meter is that it’s about 40 inches long.
Last of all, let’s compare a kilometer to a mile.
A mile is longer than a kilometer.
In fact, it takes approximately 1.6 kilometers to equal 1 mile.
The exact value is 1.609344
That means that a kilometer is only about 62% of the distance of a mile.
A good way to remember the estimated difference between a mile and a kilometer
is to multiply both by 10 and remember that 10 miles is roughly the same distance as 16 kilometers.
That fun fact may come in handy on your next road trip…
Oh, we should be at the camp site in 16 kilometers.
16 kilometers!? We’re NEVER gonna get there!!
Oh, chill back there, that’s only 10 miles.
Yes!!!
Alright, so that’s a basic overview of the most common units used to measure distance.
Hopefully, it’s given you a better idea of how big each unit is,
how the various units relate to each other,
and what sorts of objects they’re helpful for measuring.
Again, there aren’t too many exercises for this section,
but doing them will help you remember the relationships between some of these important units.
As always, thanks for watching Math Antics, and I’ll see ya next time.
Learn more at www.mathantics.com