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Exponential Notation The symbols 1 03 , 1 E3, and 10**3 all mean 10 to the third power i .e. 10 x 10 x 10. The first wa y of writing is used if the writer can do superscripts, the other ways are used in some computer notations where superscripts are n ot available More generally 1 0n means 1 0 multiplied together n times, i.e. 10x10x10...x10 where there are n repetitions of 1 0 (or equivalently 1 with n zeroes following it.). To multiply together two numbers of the form 1 0n x 1 0m , the exponents are added, e.g. 1 0n x 1 0m = 1 0m+n Similarly, 145 means 14 x 14 x 14 x 14 x 14 = 5 3 7 8 2 4 not 14x10 5 . The concept of a negative exponent, means 1 divided by e.g. 1 0-1 means the number raised to the power given 1/10 2 - 1 means 1 / 2 10-2 means (1/10) multiplied together twice, i.e. 1 0-2 =1/10 2 = (1/10) x (1/10) = 0.01 Similarly, 1 7- 3= 1/(17 x 17 x 17) = 2.035x10 -4 = 0.0002035. The rule of adding the exponents when multiplying together holds s o numbers of the form 1 0-n x 1 0m stil 1 0-n x 1 0m = 1 0-n+m = 1 0m-n or 1 0m / 1 0n= 1 0m-n In math, two negatives cancel (or two wrongs make a right, if you like), so 1 0m / 1 0-n =10m - -n= 1 0m + n There is no simple way to add exponential numbers, you need t o either write them out explicitly or factor them e.g. 1 02 + 1 04 = 100+10000=10100 =102 x ( 1 + 1 02 )=10 2 x (1+100)= 1 02 x (101)=10100 Scientific Notation This is a stylistic w ay to express values. It tells does not change the information, but it does make i t easier t o compare values and it makes it unnecessary t o write out many zeroes. The convention i s that the value is a number between 1 and 9.9999 times a n integer power of 10. So the following are written i n scientific notation 5x109 , 4.23x10-6 , l.09 x 1 04 while the following are not 50, 43.9x10-7, 0.00109 x 10 7 although they are faithful representation s of the same number values. When operating with scientific notation, the easiest thing i s to load t he values into your calculator, find the answer, and then rewrite into scientific notation.