1. Standard Notation to Scientific Notation
A number in scientific notation has two factors:
The first factor is a number less than 10 and greater than or equal to 1.
The second factor is a power of 10 with an exponent.

2. IF THE ORIGINAL NUMBER IS LESS THAN 1 THE EXPONENT WILL BE NEGATIVE.
IF THE ORIGINAL NUMBER IS GREATER THAN 1 THE EXPONENT WILL BE POSITIVE.

3. Example 1 What is 4,500,000 expressed in scientific notation?
Step 1: Write the first factor:
Place a decimal point so that the number formed by the digits is greater than or equal to 1 and less than 10.
The first factor is 4.5

4. Example 1 Continued Step 2: Find the exponent for the second factor.
Count the number of places the decimal point moved to form the first factor.
The decimal point moved 6 places to the left, so the exponent of the second factor is positive 6.
Solution: 4,500,000 = 4.5 x 106

5. Example 2 What is 0.00017 in scientific notation? Step 1:
The first factor is 1.7
Step 2:
The decimal moved 4 places to the right.
The exponent is negative 4.
Solution: = 1.7 x 10-4

6. What is 875,000,000 written in scientific notation?
Try These
What is 875,000,000 written in scientific notation?
What is written in scientific notation?

7. Example 3
The average distance between Saturn and the sun is about 875,000,000 miles. What is this number in scientific notation?
Step 1: Write the first factor:
Write the three nonzero digits in 875,000,000.
Place a decimal point so that the number formed by the digits is greater than or equal to 1 and less than 10.
The first factor is 8.75.
Step 2: Find the exponent for the second factor.
Count the number of places the decimal point moved to form the first factor.
8.75,000,000.
The decimal point moved 8 places to the left, so the exponent of the second factor is positive 8.

8. Example 3 Continued
Step 3: Write the second factor
The exponent is positive 8, so the second factor is 108.
Step 4: Write the two factors with a multiplication symbol.
8.75 x 108
Solution: 875,000,000 = 8.75 x 108