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

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

Scientific Notation Rules 4.632 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.

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.

How does Scientific Notation Work? 14 0,000,000,000 standard form 1.4 x 10? 1.4 x 1011 scientific notation What number goes here? Notice that the exponent on the base 10 is positive. That indicates a number larger than 1.

Scientific Notation: Great for very small numbers The size of a dust particle is about 0.000 000 000 752 kilograms 0.000 000 000 752 standard form 7.52 x 10? what number goes here? 7.52 x 10-10 scientific notation Notice that the exponent on the base 10 is negative. That indicates a number less than 1.

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

Using the HP 39 G Enter the following number: 3.4 x 1011 3.4 shift EEX 11 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.

Using the HP 39 G Enter the following number: 2.46 x 10-9 2.46 SHIFT EEX (-) 9

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)

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) 0.00075 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

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)

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.

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.

Terminating numbers A terminating number is a number that terminates, which means ends. Examples of terminating numbers: 3.14 4.5678932221 0.33339 Examples of numbers that do NOT terminate 3.333333… pi 0.121231234….

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: 3.33333…. 4.34343434…… Examples of NON-repeating numbers: 3.343453456….. pi 9.352109….

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.

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

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.

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