1. Applying Exponent Rules: Scientific Notation
5 Section 6
Applying Exponent Rules: Scientific Notation

2. Section 5.6 Objectives
1 Convert Decimal Notation to Scientific Notation
2 Convert Scientific Notation to Decimal Notation
3 Use Scientific Notation to Multiply and Divide

3. Scientific Notation
When a number has been written as the product of a number x, where 1  x < 10, and a power of 10, it is said to be in scientific notation. That is, a number is written in scientific notation when it is of the form
x × 10N
where
1  x < 10 and N is an integer.
8200 =  = 8.2  103
Greater than 1 and less than 10
Power of 10
34,200,000 =  = 3.42  107
Scientific notation

4. Decimal Notation to Scientific Notation
Steps to Convert from Decimal Notation to Scientific
Notation
To change a positive number into scientific notation:
Step 1: Count the number N of decimal places that the decimal point must be moved in order to arrive at a number x, where 1  x < 10.
Step 2: If the original number is greater than or equal to 1, the scientific notation is x × 10N. If the original number is between 0 and 1, the scientific notation is x × 10–N

5. Decimal Notation to Scientific Notation
Example: Write 67,300 in scientific notation.
What power?
67,300. =  10
Starting position of decimal point
Ending position of decimal point
The decimal point was moved 4 places to the left, so we use a power of 4.
67,300 =  104
A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.

6. Decimal Notation to Scientific Notation
Example: Write in scientific notation.
What power?
= 4.8  10
Starting position of decimal point
Ending position of decimal point
The decimal point was moved 2 places to the right, so we use a power of –2.
0.048 = 4.8  10–2
A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.

7. Scientific Notation to Decimal Notation
Steps to Convert from Scientific Notation to Decimal
Notation
Step 1: Determine the exponent on the number 10.
Step 2: If the exponent is positive, then move the decimal N places to the right. If the exponent is negative, then move the decimal |N| places to the left. Add zeros, as needed.

8. Scientific Notation to Decimal Notation
Example: Write 9.1  104 in decimal notation.
9.1  104
=  104
= 91,000
Move the decimal point 4 places to the right.
Example: Write 6.72  10–3 in decimal notation.
6.72  10–3
=  10–3 =
Move the decimal point 3 places to the left.

9. Multiplying Using Scientific Notation
Example: Multiply: (3  10– 4) · (8  10– 5)
Express the answer in scientific notation.
(3  10– 4) · (8  10– 5)
= (3 · 8)  (10– 4 · 10– 5)
= 24  10– 9
Use the Product Rule.
= (2.4  101)  10– 9
Convert 24 to scientific notation.
= 2.4  10– 8
Use the Product Rule.

10. Dividing Using Scientific Notation
Example: Divide:
Express the answer in scientific notation.
Use the Quotient Rule.