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In this video we will look at how the decimal number system is structured.
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This is the number system, that is used through all high school mathematics.
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In the system, the base 10 is used to write numbers.
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So how does this work?
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The basic idea is to divide the number into groups of singular,
tens, hundreds and so on.
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I will show you how this works, but first, a quick reminder of one rule of powers.
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When you raise any base to 0th power, it will be equal to 1. This is a rule that we will use in this video.
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Here we have 28 blue dots.
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We could group these dots in two groups. One group that contains
2 tens, and another group that contains 8 singulars.
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Now we can write the number in each group as 2·10¹, which is equal to
20, and 8·10⁰ which is equal to 8
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Now we have structured the total number of dots so that they are in
tens and ones.
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It is the bases that indicate how we then write the total number.
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In this example we have 2 and 8 forming the number 28, which are now written on the base 10.
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If you want to be clear on which base the number is written, you could write the base as an index right after the number.
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In this case with the base 10.
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We will do two more examples on how the decimal number system is structured.
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We will start by looking at the number 365 and write
it out with the help of the base 10
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365 = 3·100 + 6·10 + 5·1 and this we can also write as =
+ 3·10² 6·10¹ + 5·10⁰
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Again. It's important that anything raised to the 0 is always equal to 1
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Now we can clearly see why 365 is written the way it is with the base 10
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The 3, the 6 and the 5 form the number 365 with the base 10
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We will do one last example. Here we have the number 2,010,500
We can write this number in the following way:
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2·10⁶+ 0·10⁵+ 1·10⁴+ 0·10³+ 5·10²+ 0·10¹+0·10⁰
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It forms the coefficients together form the number 2,010,500 with the base 10