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We have seen that numbers can be represented by adding together multiples of powers of a particular base number. For example, we can represent the number 54 as a sum of muliples of powers of 4:
In each of the terms written within parentheses, the number that is to be used as a factor (4 in this case) is called the base, and the number that tells how many times the base is to be used as a factor is called the exponent. This is all familiar.
The numbers outside the parentheses in the expression above have a special name, too. These multipliers are called coefficients. In our example here the coefficients are 3, 1 and 2.
3
(42)
+ 1
(41)
+ 2
(40)
↑
↑
↑
coefficients
In the expression 4(103) + 9(102) + 2(101) + 1(100) what is the coefficient of 101?
