 Okay, during the last video we spoke
about how you can have quantitative and qualitative measurements and we discussed
the difference between them and then we also looked at how you can put numbers
in and out of scientific notation and now we practice that skill and really
discussed what it means to be quantitative versus qualitative. One of
the really important things about being quantitative are units. Units are the
tags that you attach to numbers- and so you could have a quantity- like mass for
example, but if you don’t put a unit to it, it doesn’t mean as much as it could.
So for example if I were to say that somebody weighed a hundred you wouldn’t
really know what that meant unless you put a tag on it. Like you said-
well they weigh a hundred pounds or they weigh a hundred kilograms.
Well there’s a difference between them. now when we look at units of measurement
we try to use ones that are used. International ones that every scientist
can understand- and unfortunately the units that we use
in the United States are often different than what it’s used internationally. Like
when we do a mass we talk about kilograms length meters time seconds. In
the United States when we talk about length we often talk about miles or feet
and these are not considered international units. Later on in the
slide presentation you’ll see that there’s a conversion between meters and
miles, meters and feet, and so it’s important that you be able to do those
conversions. We will go through specifically how you would actually do that. So here
are some what they call base units and these base units they are fundamental-
they can’t be broken down anymore- so if I’m measuring temperature of our example
temperature is measured in Kelvin time in seconds length in meters -I can’t get
any lower than that. So that’s why they’re called base units-
we can use these base units to build other units -so these are sort of like
our building blocks for other units and they’re really fundamental -meaning that
they can’t be broken down to anything less than what they are there. Now we’re
gonna do a lot of combining units together- you know a commonly combined
unit that we would do would be something like density. Density -you studied a whole
bunch of times -you’ve seen this in seventh grade you’ve seen this probably
in earth science -and density is conceptually you know- how much volume
something takes up based on its mass but mathematically when we look at it -its
mass over volume and we’ll get more into density in the units of what they mean.
So we’ll come back and we’ll look more closely at density and what a typical
mass and a typical volume is when we’re measuring density for different types of
substances. But when we look at density, one of the units of volume and volume is
actually a derived unit where you have a length times the width times the height
and so this creates a situation where you have a cubic unit. Like if we look
for example at the first square here that I have first cube. I have a length 1
meter by a width 1 meter by a height 1 meter and that gives me cubic units-
meter cubed Now what I’ve done is I’ve divided up
each of those 1 meters into 10 blocks and so we can see there’s 10 blocks here
and those 10 blocks, each one of them is smaller -each one of them is a decimeter
and so if I take this decimeter out and I enlarge it then I will have a new
block that is one-tenth the size on each length.
So I will have for each dimension -I will have 1 decimeter 1 decimeter 1 decimeter-
and so if we think about this first one each length is 1 times 1 times 1 and
they’re all meters well we would have 1 meter cubed and that’s what we have down
here. When we look at the next cube each one is 1 decimeter which is 1/10 of a
meter so we have 1/10 times 1/10 times 1/10 so this is one thousandth of a
meter cubed now. It’s also 1 decimeter- so this is 1
decimeter times 1 decimeter times 1 decimeter and so this is also 1
decimeter cubed which we call a liter. Please memorize that conversion 1
decimeter cubed is 1 liter. Now we could take just one tenth of a decimeter which
is a centimeter and we would have 1 centimeter by 1 centimeter by 1
centimeter- Now if we look at that in terms of meters then we have a
centimeter is 1/100 of a centimeter and each one of them is 1/100 of a
centimeter and so we’ll actually have instead of 1000 we’ll have one millionth
10 to the 6th of a meter cubed. but since it’s all one -sorry this should
be 1 meter just to correct this. One meter one meter one meter not one
centimeter. So this would be one millionth of a meter. If we did it in
centimeters which I’ll do down here it would be one centimeter times one
centimeter times one centimeter and that would be one centimeter cubed. So look at
what happens though-We started off with one meter- we changed the length to 1/10
look at what happened to the volume- it became a thousandth of what it was- Then
we changed the length again by 10 which is really a hundredth of a meter and now
the volume went to one millionth of a meter cubed. So my advice to you is when
you look at volumes and when you look at any units and we’re going to come back
to this again and again and again. When you change the dimension by 10 the
volume changes by a thousand. And you can see that because what we do
is we normally don’t deal with the cubic part. We deal with liters, milliliters, and
a meter cubed is actually called a kilo liter. And so we have these three units
kiloliter, liter, milliliter, and they are all one
thousandth of each other even though the dimensions that make them up or only
1/10. Now when we do conversions and we have cubic units-you’re gonna have to
cube the conversion factors. We’re gonna see that. Now let’s look at a derived
unit -density. So you know you most of you know density is equal to mass over
volume and I can have different substances like a gas for example you
know for example air -which is a mixture of different gases -the density of air is
about 1.28 grams for every one liter. So imagine a small
Seltzer bottle that’s about 1 liter inside there if I were to fill it with
air -it would be 1.28 grams. It would basically be very very
light because there wouldn’t be a lot of air in there.
Take for example though if I were to do water. Now water, the density of water at
room temperature is about one gram for every one milliliter or and I’ll show
you how to do these conversions later on this is a thousand grams for every one
liter so look at the comparison here. When I have water which is a liquid- the
density has gone up significantly. There are some solids that are really really
dense- so I would have for example let’s say gold -gold has a density of 19.3 grams for every one milliliter. Well look at what that density is -That’s
19300 grams for every one liter. So if I were to give you, for example, a
you know piece of solid gold and then ask you to say okay, well you know, what
is the, how much would this one liter of gold weigh? it would weigh 19,300 grams . That’s a lot! If we were to change that into
pounds, you would divide that by about 500 so if you divided by around
500 you would get the number of pounds that is. So if we do that really
quickly nineteen thousand three hundred divided by five hundred so we cross out
those zeros and we have about 200 divided by four that would be about a
forty pound would be about a forty pound bottle of seltzer. One literr. Imagine that?
that’s pretty crazy. If we were to do that here with water that same bottle of
water filled with just water or same bottle of Seltzer filled with just water
would be a thousand divided by five hundred and that would give you about
two pounds-and the air -well you wouldn’t even bother- changing to pounds
will be so small- So wow, look at the difference here!
Density makes up a huge difference. When we think about density it’s the mass per
volume. The more dense something is when we think about density -the more dense it
is- that means that the same volume has more mass -and that more mass is
generally due to packing of particles. How closely are they packed
together? Are they packed far apart are they pack clothes together? Well the more
dense you are, The closer the packing so more dense equals more closely packed. this may seem like common sense to you
but a few years ago they had a Regents question like this and they wanted you
to really you know break it apart and state the packing of particles and how
it affected density. Now there’s another unit that we use which I want to go into
before we end the video and that’s specific gravity. And specific gravity
basically it’s like a sink or float type of unit. What we do for specific gravity
is we say that specific gravity is equal to the density of the object whatever it
is divided by the density of a standard. Generally this standard is water so
let’s say for example I took gold and I had well 19.3 grams per centimeter cubed
that’s my gold density and I compare it to the water standard the water standard
is one gram per centimeter cubed. Well look at what happens it’s just the same
number 19.3 but now there are no units. Specific gravity is just density without
the units-but something that’s important about specific gravity is that the
comparison between your object and your standard need the same units- so you
can’t go ahead and have a situation where you put your density of your
object in grams per liter or grams per milliliter-
I’m sorry grams per decimeter cubed and your water is in grams per centimeter
cubed -it won’t work- the units have to be the same. They need the same units. So
what we’ve done so far is we’ve spoken about you know specific SI units and
just to scroll back here- the specific SI units that we talked
about were mass length time temperature there’s this unit that we
haven’t gotten into -amount of substance called a mole. We’re gonna do a lot with
moles. We call them base units -and then we also talked about how you can combine
them to make a derived unit . One derived unit is volume but there are other
derived units such as density and we can also use specific gravity basically
telling you if an object sinks or floats. So when I look at gold’s density it is
19.3, its specific gravity is also 19.3 Since the specific gravity is greater
than the density of the standard -what ends up happening is the object will
float the object will sink, sorry. If the specific gravity was less than
the standard the object would float. Now what we’re gonna do next is talk about
prefixes and honestly I don’t expect you to memorize all these but a lot of them
I expect you to know like kilo deci centi milli micro nano Pico those are
the ones that I really focus on now We’re gonna go in the next video into
this in more detail. I’m going to stop for now here and we’ll pick up with
prefixes.