Scientific Notation
Scientific notation allows us to write very big or very small numbers in manner that is easy to read.
When a number is written in scientific notation, it is made up of two parts. The left hand part is a
number that is greater than or equal to one, but less than ten, and the right hand part is ten raised to
a power. This power may be positive or negative. When the power is positive, the original number is
greater than 1, and when the power is negative, the original number is less than one. For example,
when we write 50,000 in scientific notation, it is written as 5 x 104. When we write .00008 in scientific
notation, it is written as 8 x 10-5.
Big Numbers
For a large number such as 900,000 we will be moving the decimal point to the left so that we have a
number greater than or equal to one, but less than ten. The decimal point is moved 5 places to the
left, and this is an important number to remember, because this is going to be the power we use with
10. Since we now have found that 9 is our number between 1 and 10 and our power which is 5, we
can now write 900,000 in scientific notation as: 9 x 105
If we have a number such as 456,000,000 we use the same process. The decimal point is moved to
the left until we get a number that is between 1 and 10. When we move our decimal point 8 places to
the left, we get 4.56 and our power will be 8. So 456,000,000 becomes 4.56 x 108.
Small Numbers
For a small number such as 0.000005 we will be moving the decimal point to the right so that we
have a number greater than or equal to one, but less than ten. The decimal point is moved 6 places
to the right and this too is going to be the power we use with 10, and we have found a number
between 1 and 10 and that number is 5. However when we move a decimal point to the right, the
exponent will be negative. Since we have found our number between 1 and 10 and our power, we
can now write 0.000005 in scientific notation as: 5 x 10-6
If we have a number such as 0.0000739 we use the same process. The decimal point is moved to
the right until we get a number that is between 1 and 10. When we move our decimal point 5 places
to the right, we get 7.39 and our power will be -5. So 0.0000739 becomes 7.39 x 10-5.
Moving from scientific notation to standard numbers.
If you have a number written in scientific notation, you may be asked to write it as a standard number.
A number such as 3.28 x 104 can be easily converted. All you have to do is move the decimal point
to the right the number of spaces that is the same as the power that 10 is raised to. So for this
number, you move your decimal point 4 spaces to the right, and you number is 32,800.
The process is very similar when you have negative exponents. For 9.49 x 10-5 you move the
decimal point 5 places to the left, and your number is 0.0000949