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As you can see in the example above, when we express a number as the sum of a set of multiples of powers of 10, the coefficients tell us how many 1’s, how many 10’s, how many 100’s, and so on, are to be added together to make up the number.
We can now make the point we have been approaching rather coyly for some time: In the decimal system numbers are written as a sum of multiples of powers of 10. The actual digits that are written in a decimal number are the coefficients of each power of 10 to be used, as shown below:
