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In this video we will talk about and practice on
how to use a number line.
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We will look at what a number line is and see different examples
on how numbers and intervals can be positioned on the number line.
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A number line is a way to represent or visualize
all real numbers.
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Often you position numbers on the number line
to understand how it is scaled.
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On the number line that you see before you, the number 0 is positioned.
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All numbers to the right of the number 0 are the positive numbers
and all the numbers to the left are the negative numbers.
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If we position number a and b on the number line,
then a > b when a is farther to the right than b.
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Let's take som examples where we are positioning
numbers on a number line.
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In the first example, we will position the number 100 on
this number line.
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On this number line, one step corresponds to 50, because 200 is marked 4 steps to the right of 0.
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So this is where we find number 100.
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In the next example we will position the number 3.5 on the number line.
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Here are the numbers 0 and 1 positioned and there is a vertical line
between 0 and 1.
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This gives you that every step on this
number line is equal to 0.5
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Let's position the numbers 2 and 3.
We will see that 3.5 will be positioned here.
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We will take a similar example.
Here we position the number -1.2 on the number line.
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We already have the numbers 0 and -0.3 positioned.
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We can then say that every step of the number line corresponds to 0.3.
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Let's position -0.6 and -0.9 on the number line
The number on the left should now be -1.2.
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We will finish this lesson by looking at
how to define an interval on the number line.
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An interval is containing all numbers between two different numbers.
You then use comparison operator to describe how.
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We will take this step by step and first discuss some important
things that are shown on this number line.
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First, these round end points here represents the numbers -2 and 3.
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The number a is positioned at the end of the number line.
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This means that a represents all the numbers on the number line.
We will also use a to describe the interval.
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We could have used another letter other than a, for example, x.
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Now we take a look at the dotted circle to the left.
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A dashed circle means that the point or number -2 is not included in this interval.
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Number 3 however is included in the interval.
This point has a solid line and is filled.
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Here you use the symbols ≥ and ≤ to show that
the interval can be equal to this number.
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We have now sorted out the different parts and it's time to describe our interval.
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a is greater than -2 and smaller or equal to 3.
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Using symbols, we describe it like this.
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a is grater than -2 and smaller or equal to 3.