1. Chapter 4-8 Scientific Notation
UNIT 2
Chapter 4-8 Scientific Notation

2. Scientific Notation
When you deal with very large numbers like 5,000,000 or very small numbers like , it is difficult to keep track of the place value. We can use Scientific Notation as a shorthand way of writing number using powers of 10.
A number expressed in scientific notation is written as the product of a factor and a power of 10
That factor must be greater or equal to 1 and less than 10.

3. Scientific Notation
Example: The number 5,000,000 written in Scientific Notation would look like:
5,000,000 = 5.0 x 10 6
Factor is 5 (greater than 1, less than 10)
.0004 = 4 x 10 −4
Factor is 4 (greater than 1, less than 1)

4. Express the number in Scientific Notation
60,000,000
= 6.0 x 10,000,000 {the decimal moves 7 places to the left. **If the decimal moves to the left, the exponent is positive}
= 6.0 x 10 7
= 3.9 X {The decimal moves 5 places to the right. **If the decimal moves to the right, the exponent is negative}
= 3.9 x 10 −5

5. Standard Notation
Standard Notation is simplifying the product of 2 factors
If the exponent is positive – move the decimal to the right
If the exponent is negative – move the decimal to the left
**The decimal will tell you how many times to move right or left

6. Express the number in Standard Notation
3.76 x = = 37,600 {move your decimal 5 places to the right and fill in empty spaces with zeroes}
5.1 x 10 −3 = = {move your decimal 3 place to the left and fill in empty spaces with zeroes}
7 x = = {move your decimal 2 places to the right and fill empty spaces with zeroes}

7. Let’s Try Some Examples!
Express each number in scientific notation
3,200 2)70,000 3)800,000
Express each number in standard form
4) 4.35 x ) 6.49 x 10 −6

8. Let’s Check Our Answers!
Express each number in scientific notation
3,200 2)70, )800,000
3.2 x x x 10 5
Express each number in standard form
4) 4.35 x ) 6.49 x 10 −6
43,