Hi, this is Rob, welcome to Math Antics!
In this video, we’re gonna introduce the concept of measurement
which is an important topic in math and especially in science.
We’re also gonna take a look at a particular system of measurement called “The Metric System”.
Objects have different physical properties, right? …like size, weight, volume, etc.
Well, the whole point of measurement is to quantify those properties,
which just means expressing them as a number.
Without measuring, you could say that someone is “tall” or “short”
or that a package is “heavy” or “light”.
But those are relative terms that don’t give us very specific information.
Instead, if you were to make actual measurements,
you could say that someone’s height is 130 cm,
or that a package weighs 5.2 kg.
Measurements use an actual number to describe properties like that
so that you can know them more precisely.
But, there’s a catch…
Unless you know what a centimeter or a kilogram is,
those measurement won’t be very helpful.
Centimeters and Kilograms are examples of what we call “Units of Measurement”.
Units of measurements are pre-determined quantities that we use as references
and it’s really important to be familiar with common units of measurement
so you know what various measurements mean.
Units of measurements aren’t something fundamental to math like addition and subtraction are.
Instead, they’re amounts that people invent and agree on so that we can communicate.
If fact, we could agree to use just about anything as a unit of measurement.
I could tell you that I'm 13 hot dogs tall
and my weight is 3,259 doughnuts!
The problem with those units is that hot dogs and doughnuts aren’t very consistent
and unless you and I are using exactly the same hotdogs and doughnuts to measure,
we’ll probably come up with different results.
To get around this problem, the units that we use in math and science are ‘standardized’
which means that they match official standard amounts that can be
measured over and over again to give exactly the same result.
There’s even a government agency called “The Bureau of Weights and Measures”
that defines and maintains those standard amounts.
Well… what do we have here?
Nothin’… just measurin’ stuff.
Let me see that!
Ha! Just as I suspected. This isn’t properly calibrated.
I just had it checked!
Yep, I’m gonna have to take it into the lab for adjustments.
Don’t let it happen again!
So… is there a number I call to get that back?
Of course, getting a bunch of different people to all agree
to use the same standards is not always an easy task.
And throughout history, a variety of different units have come in and out of popularity.
For example, the ancient Egyptians used units like “cubits” and “kites”,
which aren’t so popular today.
In modern times there are still a lot of different units used in different countries,
but the most popular system of units used around the world is called “The Metric System”
Well, its official name is “The International System of Units”
or “S.I. Units” for short,
which stands for the French, “Systeme International”.
But the term “Metric System” is still often used to refer to this system.
The Metric System is a really great idea because
it makes the math involved with certain measurement and unit conversion much easier to do.
That’s because, just like our Base-10 number system,
most units in the Metric System take advantage of powers of 10.
The idea behind the Metric System is to start with a base unit
and then use standard prefixes to make other units
that are bigger or smaller than that base unit by powers of 10.
Here’s a list of some of those prefixes.
To see how they work, let’s consider a key unit in the metric system called a “meter”.
A meter is a basic unit of distance (or length) and it happens to be about this long.
As you can see from our prefixes,
the unit that’s 10 times bigger than a meter is called a “dekameter”,
the unit that’s 100 times bigger than a meter is called a “hectameter”
and the unit that’s 1,000 times bigger than a meter is called a “kilometer”
But this system also has prefixes to define units that are smaller than a meter.
The unit that’s 10 times smaller, or one-tenth of a meter,
is called a “decimeter”
The unit that’s 100 times smaller, or one-hundredth of a meter,
is called a “centimeter”
and the unit that’s 1,000 times smaller, or one-thousandth of a meter,
is called a “millimeter” Get the idea?
There are also abbreviations for each of these units
to make writing them down a lot more convenient.
A meter is just abbreviates as ‘m’,
and then you put other letters in front of that for the other units.
For example, a kilometer is abbreviated ‘km’,
while a centimeter is abbreviated ‘cm’.
So why does the Metric System make working with units easier?
Well… notice the pattern we get if we put these units in order
with the largest unit on the left and the smallest unit on the right.
Each unit is 10 times bigger that the unit immediately on its right
and 10 times smaller than the unit immediately on its left.
That’s exactly the same pattern that the number places use in our decimal number system.
This diagram can give you an idea of how the units relate to each other.
For example, 1 kilometer is the same as 1,000 meters.
And one millimeter is the same as 0.001 meters (or one one-thousandth of a meter)
And because all these different units of length are based on powers of 10,
you can convert between them just by shifting the decimal point one place at a time,
which is equivalent to either multiplying or dividing by 10,
depending on which direction you shift.
2.754 kilometers
is the same as 27.54 hectometers,
which is the same as 275.4 dekameters,
which is the same as 2,754 meters,
which is the same as 27,540 decimeters, and so on…
You can convert to the next smaller metric unit by shifting the decimal point to the right,
which is equivalent to multiplying by 10.
And you can convert to the next bigger metric unit by shifting the decimal point to the left,
which is equivalent to dividing by 10.
For example, 9.8 millimeters
is the same as 0.98 centimeters,
which is the same as 0.098 decimeters,
which is the same as 0.0098 meters, and so on…
So you can see why the Metric System is so useful.
It was designed with our number system in mind which makes it easy to work with.
Oh… and even though the metric system defines a lot of different units with all these prefixes,
not all are equally popular.
For example, it’s not very common for people to use deka meters.
They’ll usually just say “10 meters” or “25 meters”
instead of saying “1 dekameter” or “2.5 dekameters”.
In fact, there’s really just 4 metric units of length that are frequently used and they are:
the millimeter, the centimeter, the meter and the kilometer.
Oh… and of course nanometers are commonly used when referring to teeny-tiny stuff
like microbes or computer chips.
A nanometer is one one-billionth of a meter!
So that’s how metric units of distance (or length) work,
but there’s another important quantity that uses this same powers of 10 prefix pattern,
and that’s mass (or weight).
Mass is a measure of how much actual matter an object contains,
which is closely related to its weight on Earth.
In the Metric System, the basic unit of mass (or weight) is technically the kilogram,
but we’re gonna start with just a plain old ‘gram’
to see how the same prefix pattern we used for length can be used for mass also.
For reference, a gram is the amount of mass equivalent to one cubic centimeter of water.
A “dekagram” is 10 times bigger than a gram.
A “hectogram” is 100 times bigger
and a “kilogram” is 1,000 times bigger.
And similarly, a “decigram” is 10 times smaller, or one-tenth of a gram.
A “centigram” is 100 times smaller, or one-hundredth of a gram.
And a “milligram” is 1,000 times smaller, or one-thousandth of a gram.
See… the same pattern is used!
And all of these units of mass have abbreviations also.
The pattern of abbreviation is similar to the metric units of length,
but instead of an ‘m’ for meters, you use a ‘g’ for grams’.
’kg’ is kilograms,
‘mg’ is milligrams, and so on…
Again, because these units of mass are based on powers of 10,
you can convert between them just by shifting the decimal point.
You can convert to the next smaller metric unit by shifting the decimal point to the right,
which is equivalent to multiplying by 10.
5.24 kilograms
is the same as 52.4 hectograms,
which is the same as 524 dekagrams,
which is the same as 5,240 grams, …and so on.
And you can convert to the next bigger metric unit by shifting the decimal point to the left,
which is equivalent to dividing by 10.
16.3 milligrams
is the same as 1.63 centigrams,
which is the same as 0.163 decigrams,
which is the same as 0.0163 grams, and so on…
But, as was the case with units of length,
many of these units of mass are not used as often as the others.
For example, centigrams aren’t as popular because
people will usually just say “10 milligrams” or “25 milligrams”
instead of “1 centigram” or “2.5 centigrams”.
The units of mass that you’ll most commonly encounter in everyday life
are the milligram, the gram, and the kilogram,
so make sure you’re familiar with those.
Alright, so that’s the basic idea behind measurement and Metric System.
Measurement helps us describe things in the world we live in and to compare them using units.
And the units in the Metric System are specially designed
to play well with our base 10 number system.
But it’s important to know that the S.I. or Metric System
does use some units that are not based on powers of 10
…like time for example.
The basic S.I. unit of time is the second,
but units of time that are larger than a second are still the traditional ones
that are based on the motion of the earth and sun like minutes, hours, days and years.
Fortunately, units of time that are smaller than a second
do use the base 10 prefixed such as milliseconds, and nanoseconds.
I wish I had more time to talk about time in this video
…and all the non-metric units that are still commonly used today like feet or pounds,
but I’m afraid those will have to wait for future videos.
There aren’t too many exercises for this lesson,
but if measurement and the Metric System are new topics for you,
you might want to give them a try.
As always, thanks for watching Math Antics and I’l see ya next time.
Learn more at www.mathantics.com