The term "exponential notation" refers generally to the practice of representing a power of a number using an exponent. Example 10*10*10 = 10^3 (Note that 10*10*10 = 1000, and that 3 is the number of zeros in 1000.) We often want to use this when representing numbers in scientific notation, or when showing the place values of digits of a number written in expanded form. (These are related activities.) Example 62345 = 60000 + 2000 + 300 + 40 + 5 = 6*10,000 + 2*1,000 + 3*100 + 4*10 + 5*1 = 6*10^4 + 2*10^3 + 3*10^2 + 4*10^1 + 5*10^0 (expanded form using exponential notation) = 6.2345*10^4 (scientific notation) To find the multiplier, determine the most significant digit. Set the other digits to zero, and set that digit to 1. Examples 62,345 saving only the most significant digit is 60,000. With the most significant digit set to 1, it is 10,000. 0.003498 saving only the most significant digit is .003. With the most significant digit set to 1, it is .001. Once you have the multiplier, determine the power of 10 that it is. This is related to the number of places you must move the decimal point before the value becomes equal to 1. If you started with a value less than 1, the exponent will be negative. Examples 10,000 becomes 1 after we move the decimal point 4 places to the left. 10,000 = 10^4. .001 becomes 1 after we move the decimal point 3 places to the right. .001 = 10^-3. The example numbers above, when written in scientific notation, become 6.2345*10^4 3.498*10^-3 Note that the decimal point is now immediately to the right of the most significant digit. The multiplier makes this number equivalent to the original.