Scientific Notation
Scientific notation is a unique representation of very large or very small numbers
involving multiplication and powers of ten. Writing numbers in this fashion saves time
and space. This section will contain the steps to writing numbers in scientific notation
and how to multiply and divide with such numbers.
Writing Numbers in Scientific Notation
Very small or very large numbers may be written in scientific notation. Each number is
adjusted to be a number between 1 and 10 and is multiplied by a power of ten.
For example, the distance from the sun to earth is 93, 000,000 miles. In scientific
notation, 93,000,000 = 9.3 x 10 to the seventh power. Another example is
567,000,000,000,000,000,000 is written as 5.67 x 10 to the 20th power…much easier! If
the decimal is moved 20 places to the right the original number results. Remember, a
number in scientific notation is written as a product of a number between one and ten and
a power of ten.
Example: Write 56,000 in scientific notation.
Step 1: To write a number in scientific notation, place the decimal between the first and
second digit. 56,000 -> 5.6000 -> 5.6. 5.6 is now a number between 1 and 10.
Step 2: Count the number of places the decimal must move in order to be in its original
position.
5.6000 -> 4 places to the right
Step 3: Multiply the number by a power of 10 equal to the number of places counted.
Hint: 4 places to the right = 10 to the 4th.
4 places to the left = 10 to the -4th.
5.6 must be multiplied by 10 to the 4th so 56,000 is the result.
56,000 = 5.6 x 10 to the 4th
Example 2: Write 0.00000081 (81 hundred millionths) in scientific notation.
Move the decimal between the 8 and 1 and count the places to the left needed to place the
decimal back in its original position.
0000008.1 -> 8.1 x 10 to the -7th
(A negative power of 10 moves the decimal left).
Example 3: Write 0.0000456 in scientific notation.
= 4.56 x 10 to the -5th
Multiplying and Dividing with Numbers Written in Scientific Notation
It is also possible to use scientific notation as another approach to multiplying and
dividing large and small numbers. This section contains steps to multiplication and
division using scientific notation.
Try a few more
Solve using scientific notation and write answer in standard form as well
(610)(2,500,000,000)
(6.1 X 102)(2.5 X 10 9)
(6.1 X 2.5) (102 X10 9)
(15.25 X 10 11
1.525 X 1012 or 1,525,000,000,000