1. Scientific Notation Rational and Irrational Numbers
Power point notes to accompany Lesson 1 Semester 2

2. 4.632 x 106 Scientific Notation Exponent is 6 Coefficient is 4.632
Baseis 10
The number 4 is the coefficient

3. Scientific Notation Rules
x 106
The coefficient is always larger than or equal to 1, and smaller than 10.
The base is always 10.
The exponent is positive for large numbers, and negative for numbers between 0 and 1.

4. Why use Scientific Notation?
The speed of light is 300,000,000 m/sec
The speed of light is often represented by the letter c.
It is a large number used in many calculations (E = mc2)
In scientific notation it is written 3.0 x 108
It is easier to calculate with large numbers in scientific notation.

5. How does Scientific Notation Work?
14 0,000,000, standard form
x 10?
1.4 x scientific notation
What number goes here?
Notice that the exponent on the base 10 is positive. That indicates a number larger than 1.

6. Scientific Notation: Great for very small numbers
The size of a dust particle is about kilograms
standard form
x 10? what number goes here?
7.52 x scientific notation
Notice that the exponent on the base 10 is negative. That indicates a number less than 1.

7. What does Scientific Notation look like on the HP 39G ?
Find the EEX key
To access these second functions, you need to hit the SHIFT key

8. Using the HP 39 G Enter the following number: 3.4 x 1011
shift EEX enter
Standard form: 340,000,000,000
Notice that both the scientific form and the standard form are displayed on the screen
Notice that the number 10 was not entered by pushing a 1 and a 0.

9. Using the HP 39 G
Enter the following number:
x 10-9
SHIFT EEX (-) 9

10. The sun is about (1. 5 x 1011) meters from the earth
The sun is about (1.5 x 1011) meters from the earth. Light travels at approximately (3.0 x 108) meter/sec. How many seconds does it take for light to travel from the sun to the earth? (distance = speed x time)
50 seconds
5.0 x 102 seconds
5.0 x 103 seconds
Answer is b) 500 seconds. Distance = (speed) (time)

11. Thiomargarita namibiensis is the largest known species of bacteria and is approximately 7.5 x 10-4 m wide. The average bacterium is about the size of Escherichia coli and is about 1.5 x 10-6 m wide. What is the difference in widths of the two species?
74.9 x 103 m
7.5 x 10-1 m
7.5 x 10-4 m
Answer: c) meters. Thiomargarita namibiensis was discovered in 1999 and is the largest known bacterium in the world. It is about the size of the period at the end of this sentence.
E. coli
T. namibiensis

12. Solve and express the answer in scientific notation:
( 2.45 x 105 ) x (5 x 103 )
1.225 x 109
12.25 x 108
1.225 x 1015
12.25 x 1015
Answers b) and d) are not in scientific notation because the coefficients are larger than 1. Correct answer is a)

13. Classifying Numbers Numbers can be classified
For instance, we can pick out all of the numbers that are divisible by 2. They are classified as even numbers.
We can also classify numbers in other ways.

14. Rational and Irrational
Numbers can be classified as rational numbers.
Rational numbers are numbers that can be written as fractions.
In decimal form, rational numbers are either terminating or repeating.

15. Terminating numbers
A terminating number is a number that terminates, which means ends.
Examples of terminating numbers:
Examples of numbers that do NOT terminate
… pi ….

16. Repeating Numbers
A repeating number is a number that does not terminate, but it repeats over and over EXACTLY THE SAME
Examples of repeating numbers:
… ……
Examples of NON-repeating numbers:
… pi ….

17. Rational vs. Irrational
If a number in decimal form repeats exactly, or terminates, then it is a rational number.
If a real number is NOT rational, then it is irrational.
Real numbers are either rational or irrational.

18. Real = Rational + Irrational
Real Numbers
Another classification of numbers is the set of numbers called Real Numbers.
This one is easy. Real numbers are the rational numbers and the irrational numbers combined.
Real = Rational + Irrational

19. Place the following numbers in order from least to greatest.
-7, 14/3, 280%, 1 3/7
Step 1. Change into decimals.
Step 2. Place on a number line.

20. Order from least to greatest: -7, 1 3/7, 280%, 14/3
-7 = -7
14/3 = 14 divided by 3  4.7
280% = 280 divided by 100  2.8
1 3/7 = 1 + 3/7  1.43 -7
14/3
1 3/7
280%
Order from least to greatest: -7, 1 3/7, 280%, 14/3