1. Objective The student will be able to:
express numbers in scientific and standard form (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. 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

5. 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

6. Express 1,430,000,000 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
1.43
The decimal was moved how many places? 9
The answer is now in scientific notation.
1.43 x 109

7. Express 0.00000000004 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
After the 4
The decimal was moved how many places? 10
When the original number is less than 1, the exponent is negative.
4 x 10-10

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

9. Express 5.5 x 10-3 in decimal notation.
.0055
Express 2.09 x 1012 in decimal notation.
2,090,000,000,000

10. Comparing numbers in scientific notation:
Order the numbers by the powers of 10.
Arrange the numbers with the same power of 10 in order by their decimal parts.

11. Simplify. Write each answer using scientific notation.

12. Simplify. Write each answer using scientific notation.

13. Simplify. Write each answer using scientific notation.

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.