# Lesson 2: Scientific Notation

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

Discovery question:

Mirabilis pollen grain

Myosotis genus pollen grains

How many times larger is Mirabilis pollen grain (0.00025m) than Myosotis genus pollen grain (0.000002m)?

1. Write numbers as scientific notation.
2. Divide larger number by the smaller
3. 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. 1.41*10^7
2. 7.49*10^7
3. 1.06*10^8
4. 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:

Next on “math class”:
• Homework review
• Powers with same base multiplied, but how?
• We will discover that tomorrow…