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.