Because the real numbers include both the

rational numbers and the irrational numbers sometimes it can be kind of a challenge to

show or express all the real numbers at once. Especially in any sort of like logical order

because we have fractions and decimals and whole numbers and sometimes its hard to tell

what’s bigger than what. And to show or layout these numbers in any meaningful sense can

be a challenge so one way that’s a great way to show the real numbers is on whats called

a number line specifically a real number line we use these all the time

in algebra. So it would be good for us to get comfotable using these guys. So basically

it looks like this, basically you have zero in the middle of your number line and then

all the positive numbers are listed to the right of zero, and all the negative numbers

are listed to the left of zero. And just as points of reference, we usually put tick marks

on all the integer values. So we’ll have zero, then we’ll have one, and then two, and then three, four, five, six, etc… And then that’s

not saying that these are the only numbers on the number line, these are just simply

points of reference. And to the left of zero we would have negative one, negative two,

negative three, negative four, negative five, negative six, etc… And it extends out beyond

six, but at some point you just run out of space and so if you see these arrows on the

end right here, that indicates that the number line continues out father than I am really

drawing. And again just to be clear, I am not saying that these are the only numbers

on the number line. There are numbers here, and here, and everywhere. The ticks marks

are just meant to be simply points of reference. So if you want plot a number on a number line

that’s showing a reader where it is in relation to the other numbers on the number line. For example, if we plotted a number at five,

we would go out to five, we would put a dot and then we plotted five. We’ve shown the

number five on the real number line especially showing where it is in relation to other numbers.

For example I know that it’s greater than zero, but its less than six because its after

zero, but is before six as you read the number line from the left to the right. So just for

some practice, let’s practice plotting a few points. So I’ve labeled these points A, B,

C, D, and E. Let’s quickly just go through and plot them real quick. To plot the point

A, we would go to three, so we’ll start at zero on the number line, and would go right,

one, two, three units. We go to the right because three is a positive value, if we want

to plot B so this is A right here. So if we want to plot B we’ll go left two and a half

units that’s negative two point five. So we will start at zero and go left one,

two point five, that’s half a unit. So you can certainely plot points between tick marks.

So this would be B. C is a zero, you can have points plotted at a zero that’s totally fine

as well. Sometimes you will get fractions like thirteen-halves. Thirteen-halves if you

just use long division or a calculator and divided thirteen by two, you would get a decimal

of six point five. Six point five is halfway between six and seven. So you would go to

the right six and a half units and this would be where D is, and then E, you can even have

very intricate decimals like negative four point eight seven one now this kind of strains

the limits of capabilities. There is definately a point – negative four point, eight, seven,

one, on the number line. But the best we can really do with just pencil and paper is that

we’d know this is just shy of negative five. So I know it’s between negative four, negative

five, probably a little closer to negative five, because negative four point eight seven

one is a little closer to negative five than it is to negative four. So about the best

we can do just eyeballing it is putting it just short of negative five, and we will call

that point E. So anyways the real number line we use this all the time to plot real values

and especially to show them in relation to one another.

Thank you so much!

Thank you so much! It was helpful ðŸ™‚