What is expanded form,exponential notation and scientific notation?

The number system we use is a "place value" number system. That means the value of a given digit changes depending on where it is found in the number. This is one of the first things you learn when you learn to write numbers. The digit 1, for example, can stand for a single unit, 10 units, or 100 units, or any of an infinite number of other numbers of units.  "Expanded form" is a way to write a number as a sum such that each term in the sum represents the place value of one of the digits in the number. It is so simple that it is sometimes difficult to understand why we would be interested in doing this. Example   1234.56 = 1000 + 200 + 30 + 4 + .5 + .06  "Expanded form" can also be written a couple of other ways to better show off the multiplier associated with each decimal place. Example   1234.56 = 1*1000 + 2*100 + 3*10 + 4*1 + 5*.1 + 6*.01  This form can also be written "using exponents". This actually gives some insight into powers of 10 that can be useful when studying scientific notation and logarithms. Example   1234.56 = 1*10^3 + 2*10^2 + 3*10^1 + 4*10^0 + 5*10^-1 + 6*10^-2   Note the nice progression of powers from 3 down to -2, including 0.  Scientific notation builds from the first term of the "expanded form using exponents." Everything beyond the first digit becomes part of the decimal fraction portion of the number in scientific notation. Example   1234.56 = 1.23456*10^3