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In this video we will go through and practice how to use a number line.
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We will take a look at what a number line is, and view some examples of how numbers and intervals are marked on a number line.
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A number line is a way to represent or visualize all real numbers.
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Usually you mark a few numbers on the number line, to show how the number line is graded.
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On this number line displayed, number 0 is marked.
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This means that all the numbers on the righthand side of the marked zero are positive numbers, and all the numbers on the left side are negative numbers.
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If we mark a number a and a number b on the this number line, we get that a is greater than b, since number a is placed to the right of number b.
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We´ll do some examples where we mark numbers on a number line.
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In the first example, we will mark number 100 on this number line.
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Here, one step in either direction equals 50, since number 200 is marked four steps to the righthand side of zero.
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Consequently we find number 100 here.
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In the next example we´ll mark number 3,5 on a number line.
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Here, numbers 0 and 1 are marked and there is a vertical line in-between them.
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Thereby every step on this number line represents 0,5.
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If we mark number 2 and 3 we can see that number 3,5 thereby should be placed here.
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We´ll do one more similar example. Here we will mark the number -1,2 on the number line.
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We were already given the marked numbers 0 and -0,3.
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We can thereby say that every step on this number line represents 0,3.
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Now, we´ll mark numbers 0,6 and -0,9 on the number line, and the number to the left should thereby be -1,2.
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We will end this lesson by looking at how to describe an interval on a number line.
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An interval include all possible numbers between, for example, two numbers. To describe this, you use inequality-symbols.
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Let us take this step by step and initially discuss a few important things on this number line displayed.
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To begin with, we can conclude that these round endpoints represent numbers -2 and 3.
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Letter a is also written in the end of the number line.
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This means that letter a represents all numbers on the number line. Therefore letter a will also be used in our expression for this interval.
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We could also have used a different letter than a, such as x for example.
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Now let´s take a look at the dashed circle to the left.
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That it´s dashed means that the dot/number 2, is not included in the interval.
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Number 3, on the other hand, is included in this interval, since the dot is filled complete.
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This is when you use the symbols ≥ and ≤, to describe that the interval can be equal to this number.
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Now we have sorted out the different parts, ad it´s time to describe our interval.
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Here is consequently a greater than -2 and less than, or equal to 3.
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With symbols we describe it like this.
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That is; a is greater than -2 and less than, or equal to 3.