Notes: Scientific Notation
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Why use scientific notation? Scientific notation is used to write very large numbers or very small
numbers without having to write many digits. Scientific notation helps us understand how large or small
a number is in terms of powers of ten.
The first number in scientific notation is known as the coefficient. In scientific notation, the absolute
value of the coefficient must be greater than or equal to 1 and less than 10.
The second number is a power of ten.
Example:
Speed of light = c = 3.00 x 108 m/s = 300,000,000 m/s
Diameter of a red blood cell = 7 x 10-6 m = .000007 m
Converting Standard Numbers to Scientific Notation
1. Place the decimal so that the original number is now between 1 and less than 10.
2. Count how many decimal places you would have to move to restore the number back to its
original form. This partially determines the exponent of 10.
3. If you have to move to the right to restore the number, the exponent of 10 is positive.
If you have to move to the left to restore the number, the exponent of 10 is negative.
Write the following number in scientific notation
524,000,000
Write the following number in scientific notation
0.00000000037
Write the following number in scientific notation
276,000,000,000
Write the following number in scientific notation
0.000000000374
Converting Scientific Notation to Standard Numbers
1. Locate the decimal.
2. If the exponent of ten is positive, move the decimal to the right according to the power of ten.
If the exponent of ten is negative, move the decimal to the left according to the power of ten.
Write the following number in standard form
6.02 x 109
Write the following number in standard form
3.27 x 10-8
Write the following number in standard form
5.6 x 1010
Write the following number in standard form
7.42 x 10-6
Multiplying Two Numbers in Scientific Notation
1) Multiply the coefficients.
2) Multiply the powers of ten by adding the exponents.
(1.3 x 103) (2.4 x 106)
(2.1 x 107) (1.7 x 10-4)
Dividing Two Numbers in Scientific Notation
1) Divide the coefficients.
2) Divide the powers of ten by subtracting the exponents.
(7.8 x 103) / (1.6 x 106)
(5.2 x 107) / (1.3 x 10-4)
The weight of a newborn baby panda weighs 2.2 × 10-1 pounds. If a an adult
panda can weigh up to 1.2 × 103 times more than a newborn panda, how much
does an adult panda weigh?
A farm that has
acres of land produces 1.6 ×
pounds of rice each
year. What is the average amount of rice planted per acre?