**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

**Discovery question:**

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

- 8.3*10^5
- 4.12*10^22
- 7.1*10^-5

**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.

- 0.23*10^-3
- 2.3*10^7
- 9.3*100^9

**Exercise 1:**

- 53*10^4
- 3.42^10^-7
- 0.35*100

**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

- 678,000
- 0.000032
- 51,400,000
- 0.0000007

**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

- 5.23*10^7
- 4.6*10^-5
- 2.09*10^-4
- 3.8*10^12

**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**

- 1.41*10^7
- 7.49*10^7
- 1.06*10^8
- 1.8*10^8

**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

**Homework:**

- 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…