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.