Previously on “math class”:
- exponents can be positive, 0 or negative
- anything to 0 power equals 1
- negative exponent means inverse 5^-2=1/5^2
- You can write out exponents and simplify expressions with algebra
- inverse of inverse cancels itself 1/1/5=5
- multiple of double inverse goes to multiply the number 2/1/5=2*5
Lesson 2: Scientific Notation
Today’s Learning Method: Direct Lesson, Take good notes, Write down and solve exercises. Exercises 1, 2 and 3 will be graded. You can use computer until the independent work time.
You will need:
- Paper and pen for notes and exercises
- Scientific calculator
- Computer is optional
Scientific Notation is used by scientists to write down very small and very large numbers.
- Number of seconds in a year 31,596,260 = 3.16*10^8
- Thickness of a hair 17 micrometers = 17 microns = 1.7*10^-7
- Diameter of the earth 12,715 km = 1,2*10^7
- Distance between the sun and the Saturn
- Radius of an atom
How many times larger is Mirabilis pollen grain (0.00025m) than Myosotis genus pollen grain (0.000002m)?
- Write numbers as scientific notation.
- Divide larger number by the smaller
- Express in scientific notation
Don’t worry if you don’t get it right. Give it a go.
Main point 1: Definition of Scientific Notation
A number in scientific notation is written as the product of two factors in the form a * 10^n. n is an integer and 1 ≤ a < 10. Examples
Main point 2: Scientific Calculator and Scientific Notation
- Scientific calculator expresses scientific notation like this: 1.35E8 means 1.35*10^8=135,000,000.
- EE key lets you input an exponents for a power of 10.
Enter 4*10^6 by entering 4 EE 6.
Example 1: How to find out if a number is in scientific notation
Is the number written in scientific notation? If not, explain.
Main point 3: To convert large number to scientific notation, move decimal point left. Exponent is positive
Example 2: How to write a number using scientific notation
Distance between the sun and the Saturn is 1,430,000,000 km = 1.43*10^9.
- Move the decimal point 9 places to the left.
- Remove unnecessary zeros
Main point 4: To convert small number to scientific notation, move decimal point right. Exponent is negative
The radius of an atom: 0.0000000001 = 1*10^-10
- Move the decimal point 10 places to the right and use -10 as exponent.
- Remove the zeros before the 1.
Exercise 2: Write these in scientific notation
Example 3: How to write a number in standard notation
Weight of an Asian elephant is 5.5*10^6g
- Move the decimal point 6 places to the right.
Main point 5: To convert scientific notation with positive exponent, move decimal point right.
Weight of an ant: 3.1 * 10^-3 g = 0.0031
- Move decimal point 3 places to the left.
Main point 6: To convert scientific notation with negative exponent, move decimal point left.
Exercise 3: Write in standard notation
Main point 7: a * 10^0 = a
Main Point 8: Comparing numbers in Scientific Notation is easy: First the exponents, then the decimal parts.
Example 4: Surface areas of 4 major oceans from smallest to the largest
Exercise 4: Arrange these atom part weights from smallest to the largest
- neutron: 1.675*10^24
- electron: 9.109*10^-28
- proton: 1.673*10^-24
- Complete all of the exercises 1, 2, 3 and 4. All exercises on the work sheet.
- Review this lesson at theprofessort.com
- Prepare for the next class by watching this video: http://www.khanacademy.org/math/arithmetic/basic-exponents/v/exponent-rules-part-1
Just watch the first 4 minutes.. We will talk about these tomorrow.
- Watch this powers of 10 video to see the scientific notation that goes along with the journed to cosmos and back.
Next on “math class”:
- Homework review
- Powers with same base multiplied, but how?
- We will discover that tomorrow…