



 
Hi Kent. "Exponential form" simply means a numeric form involving exponents. One way to write such a number is by recognizing that each position represents a power (exponent) of 10. So you can first break it up into separate pieces. I will use my own number 5 625 702: Each of these is a multiple of the number with a 1 in front: and each of these is a power of ten, so you can write the exponent which 5 625 702 = 5 x 10^{6} + 6 x 10^{5} + 2 x 10^{4} + 5 x 10^{3} + 7 x 10^{2} + 2 x 10^{0} That last one may not really be necessary. 10^0 is equal to 1, so really we are just saying 2 x 1. That is one expanded exponential form. Another way to represent a number using exponents is to write it as a product of prime numbers. Any positive integer above 1 is the product of a unique set of prime numbers. I know that the number 26 460 is 2 x 2 x 3 x 3 x 3 x 5 x 7 x 7. So written using exponential form as a product of primes, I write 26460 = 2^{2} x 3^{3} x 5 x 7^{2} The exponents reflect how many times that prime number appears as a factor. There is also an exponential form called "scientific notation" which is used extensively in science. That is simply a matter of counting how many digits you need to move the decimal place in order to have a number between 1 and 9.999... So for 5 625 702, I would move the decimal place to 5.625 702, which is 6 places leftwards from where it was. Thus, I say that 5 625 702 in scientific notation is writting 5.625 702 x 10^{6}. I hope this gives you a good idea of how to write things in exponential forms. Cheers,  


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