Scientific Notation
I. Scientific Notation
A. Scientific Notation is used
B. Examples
1. The mass of one gold atom is .000 000 000 000 000 000 000 327 gram
2. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen
atoms
C. Scientists can work with very large and small numbers much more easily if they are
written in scientific notation.
II. How to Use Scientific Notation
A. In scientific notation, a number is written as the product of two numbers: a
coefficient and 10 raised to a power.
B. For example: The number 4,500 is written in scientific notation as 4.5 x 103.
The coefficient is 4.5. The coefficient must be a number greater than or equal to 1
and smaller than 10.
The power of 10 or exponent in this example is 3. The exponent indicates how
many times the coefficient must be multiplied by 10 to equal the original number of
4,500.
C. If a number is greater than 10, the exponent will be positive and is equal to the
number of places the decimal must be moved to the left to write the number in
scientific notation.
D. If a number is less than 10, the exponent will be negative and is equal to the
number of places the decimal must be moved to the right to write the number in
scientific notation.
E. A number will have an exponent of zero if the number is equal to or greater than 1,
but less than ten.
F. To write a number in scientific notation:
1) Move the decimal to the right of the first non-zero number.
2) Count how many places the decimal had to be moved.
3) If the decimal had to be moved to the right, the exponent is negative.
4) If the decimal had to be moved to the left, the exponent is positive.
G. To emphasize again: the exponent counts how many places you move the decimal
to the left or right.
