Welcome back to lesson 1. We are in the
process of discussing real numbers in
the last video and subsets of real
numbers. Now we're going to transition
this to a more mathematical form that
you're accustomed to seeing. So we're
going to start with the most basic
representations of real numbers and
that's through a real number line. Now
many of you may remember through your
experience in pre-algebra and maybe even
further into middle school math the
different ways to plot points on a
number line and graph various things
through the use of a number line. The
number line also gives us some some real
useful tools to help with adding and
subtracting numbers, applying negative
numbers to operations and so the number
line is very effective tool. Now as you
can see the number line that we have on
this page we are just representing the
integers with little tick marks. What we
need to remember is that the space
between the integers are filled with
infinite amount of numbers of irrational
and rational numbers. Numbers that can
be represented in a decimal form whether
they repeat terminate or neither are
still represented on the real number
line. They're just not typically shown in
the general structure of the number line.
So we're just going to take a little
short lesson here on reminding ourselves
how to plot points on a number line. We'll just go down to the next part here
and what you're going to see is the
general structure of these note taking
guides where we give you an example and
then after giving you an example we're
going to ask you to work a problem on
your own. So sample you see example
number one and then you can see sample
problem number one which is a problem
that you will work. Now for this
particular problem we're just doing a
basic plotting of points on a number
line and you can see that we have a
variety of different types of numbers
now we have negative four-thirds we have
square root of two and we have 2.7. Now what I'm going to recommend to
you just for ease
of plotting these points is to start
just by simply converting to decimals.
That's going to give you a better sense
of where the value is going to show up
on the number line so maybe if you look
at the square root of two and you're
like I don't even really know where that
should go you can use your calculator to
convert that to a decimal find that it's
roughly 1.41 and plot the
value on the number line. Now notice that
that value is not labeled as one point
four one we still label it as the square
root of two, but converting it to a
decimal first just to find its location
is very useful tool. So you can see here
we have example one if I wanted to
convert to decimals I would put in
negative four-thirds in my calculator to
get a decimal and plot the point. Same
thing with the square root of two so
what I want you to do at this point now
is pause the video, take a much time as
you need to plot the points for sample
problem number 1. When you finish
plotting the points for sample problem
number 1 play the video again and
you'll watch my demonstration of working
the problem. OK, so you should have
paused the video and worked sample
problem number 1, so I'm gonna go ahead
and do that now so I'm gonna look at
this I'm gonna see square root of seven
well I'm not sure where that's going to
be on the number line so I'm going to
come back here and I'm gonna hit the
square root symbol now it is a control
and you can see that it is a second
function there and it gives me a little
box to put in so I want to do the square
root of seven square root of seven and
I'm just gonna hit enter and of course
on my calculator it just gives me right
back square root of seven so if you
recall I need to put a decimal point in
the operation somewhere so that it'll
give it to me as a decimal point. Now I know
that I can't get exactly two point six
four five seven five and on and on and
on so I just need to rough estimate of
2.6.
So we'll look at this I'm gonna get a
rough estimate of about 2.6 but I'm not
going to label it 2.6 I'm actually gonna
label it as the square root of seven and
so I can say that that one's done. I need
to label negative two and of course
that's already labeled for me through
the integers. How about negative 7/3
let's try that one so I'm gonna use the
little negative symbol and you can see
whenever I hit a button on this program
it shows a little red highlights it with
red so you can see what I just press.
I'm going to do negative 7/3 and of course I
wanted it as a decimal so that's
-2.3 so I'm gonna go
-2.3 roughly but I'm
gonna label it as negative 7/3 I have
five halves so if I do 5/2 in decimal I
get two and a half some of you may have
already known that. Now of course that's
going to be real close to my square root
of seven so I'm gonna label that below
so it doesn't get confusing and then
last but not least I have 0.75 and since
it was given to me as 0.75 I'm gonna
label it as 0.75. And so we've labeled
all of our points on the number line.
Very good, now let's look at Part B. In
Part B they want us to order the actual
temperatures so go ahead and pause the
video at this point and go ahead and
work the problems and then when you
finish working the problems play the
video to see the demonstration. OK for
Part B we're going to be ordering the
temperatures from least to greatest, very
important that you read the language and
understand what that means so we want to
put our smallest temperatures first and
then go to the highest temperatures.
We're going to start with negative two
and sometimes I find when I'm ordering
something like this I find that it's
useful to scratch out the ones that have
already used. Now we need to tell how
many temperatures were at or below zero
degrees.
So there were actually two temps that
were there and if I wanted to actually
show that set of numbers I would use the
little brackets so we had negative two
degrees and we had zero degrees. And for
mathematical purposes we're probably not
going to put the degree value in there
with it. So that is a basic use of
ordering numbers without the use of a
number line. OK, so that concludes this
lesson of using real numbers on a number
line. In the next video to finish Lesson
1 we will be discussing real number
properties
