How do write 20,508 in expanded form using powers of 10 and using exponents? Please explain the answer.


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Oddman answered
There are several ways to write a number in expanded form. One of the simplest is to express the number as a sum of numbers each having only one non-zero digit.
  20,508 = 20,000 + 500 + 8
The point of such an exercise is to help you understand "place value". This means that the value of a number's digit depends on what place in the number it occupies. The places are assigned values relative to the decimal point.
By the time you are able to write and say 2-digit numbers, you understand that the 2nd place to the left of the decimal point is the "tens" place, for example. You know each ten represents 10 ones.
By the time you can write and say 3-digit numbers, you recognize the 3rd place to the left of the decimal point is the hundreds place, and that each hundred represents 10 tens.
Your number 20,508 can be written in a way that shows that multiplication by 10 for each place further left from the decimal point.
  20,508 = 2*10*10*10*10 + 5*10*10 + 8
Whenever we have a string of factors that are all the same, we can shorten the way we write it by using an exponent.
  20,508 = 2*10^4 + 5*10^2 + 8
For completeness, we can put in the zero digits and use an exponent on the units digit. Note that the power of 10 decreases by 1 for each place we move to the right. (This continues as you go to the right of the decimal point. For example, 0.3=3*10^-1.)
  20,508 = 2*10^4 + 0*10^3 + 5*10^2 + 0*10^1 + 8*10^0

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