1. Objective The student will be able to:
express numbers in scientific and decimal notation.
Designed by Skip Tyler, Varina High School

2. How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

3. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

4. How to Use Scientific Notation
In scientific notation, a number is written as the product of two numbers…..
…..a coefficient and 10 raised to a power.

5. Rules to Remember!
If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
positive
left

6. Rules to Remember!
If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
negative
right

7. A number will have an exponent of zero if:
….the number is equal to or greater than 1, but less than 10.

8. 1. Move the decimal to the right of the first non-zero number.
To write a number in scientific notation:
1. Move the decimal to the right of the first non-zero number.
2. Count how many places the decimal had to be moved.
3. If the decimal had to be moved to the right, the exponent is negative.
4. If the decimal had to be moved to the left, the exponent is positive.

9. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1

10. 2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023

11. 1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places? 8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8

12. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

13. 2) Express 1.8 x 10-4 in decimal notation.
3) Express 4.58 x 106 in decimal notation.
4,580,000
On the graphing calculator, scientific notation is done with the button.
4.58 x 106 is typed

14. 4) Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2
Type
You must include parentheses if you don’t use those buttons!!
(4.5 x ) (1.6 x )
Write in scientific notation.
x 10-3

15. 5) Use a calculator to evaluate:. 7. 2 x 10-9. 1
5) Use a calculator to evaluate: x x 102 On the calculator, the answer is:
6.E -11
The answer in scientific notation is
6 x
The answer in decimal notation is

16. 6) Use a calculator to evaluate (0. 0042)(330,000)
6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is
1386.
The answer in decimal notation is
1386
The answer in scientific notation is
1.386 x 103

17. 7) Use a calculator to evaluate (3,600,000,000)(23)
7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is:
8.28 E +10
The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000

18. Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

19. Write in PROPER scientific notation
Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x 109
2.346 x 1011
9) x 104
on calculator: 642
6.42 x 10 2

20. Write 531.42 x 105 in scientific notation.

21. Practice Problems ANSWERS PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2
Put these numbers in scientific notation.
PROBLEMS
1.2 x 10-4
1 x 103
1 x 10-2
1.2 x 101
9.87 x 10-1
5.96 x 102
7.0 x 10-7
1.0 x 106
1.26 x 10-3
9.88 x 1011
8 x 100
ANSWERS
.00012
1000
0.01 12
.987
596
1,000,000
987,653,000,000 8

22. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
4.9 X 102
3.75 X 10-2
5.95 X 10-4
9.46 X 103
3.87 X 101
7.10 X 100
8.2 X 10-5
490
.0375
9460
38.7
7.10

23. Using Scientific Notation in Multiplication, Division, Addition and Subtraction
Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

24. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Multiplication
When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply 3.2 x Add the exponents
Answer: 6.7 x 102

25. Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Division
Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.
Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Solution: Divide 6.4 by Subtract the exponents 6 - 2
Answer: 3.8 x 104

26. Addition and Subtraction
To add or subtract numbers written in scientific notation, you must….express them with the same power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)
Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other.
5.8 x 103 = .58 x so .58 x x 104 =?
Answer: x 104