Introduction video: https://www.youtube.com/watch?v=Wf- HlVqZPHY Scientific Notation Introduction video: https://www.youtube.com/watch?v=Wf- HlVqZPHY

 Today Is… Wed, Oct 24 Neon/Flouresent Day Announcements: Red Ribbon Week Tues – Wear RED Wed – Neon Day Thurs – Hat Day Friday – Lovinggood/Hillgrove Spirit wear HW: Finish worksheet Today in class students will be learning…. how to calculate square and cube roots because carpenters, engineers, and architects use them daily in their profession.

Is always a power of 10. The power of the exponent tells you how many places to move the decimal. A number that is greater than or equal to 1 and less than 10. It may or may not be a decimal.

Course 3 4-4 Scientific Notation An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers.

Vocabulary 4-4 Scientific Notation scientific notation Word Definition Course 3 4-4 Scientific Notation Vocabulary Word Definition scientific notation A form of writing very large & very small numbers. Written as: Decimal number greater than or equal to 1 and less than 10. Multiplied by power of 10. Ex: 1800 = 1.8 x 103

Course 3 4-4 Scientific Notation Positive exponents make the decimal larger because you are multiplying by powers of 10 (move to right). Negative exponents make the decimal smaller because you are dividing by powers of 10 (move to left). REMEMBER: A negative exponent is the same as dividing by that number with a positive exponent. EX: 10-3 =

Course 3 4-4 Scientific Notation A number less than 1 will have a negative exponent when written in scientific notation. Helpful Hint

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #1 Translating Scientific Notation to Standard Notation Write the number in standard notation. 1.35  105 = 100,000 Note: There are 5 zeroes, which are represented by the exponent. 5 1.35  10 5 1.35  100,000 Think: Move the decimal right 5 places because I am multiplying by a power of 10 and there are 5 zeroes represented by the exponent. 135,000

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #2 Translating Scientific Notation to Standard Notation Write the number in standard notation. 10 = –3 1 1000 2.7  10–3 To Standard Notation: 1.) Write the decimal. 2.) Move the decimal point the number of places given by exponent. - Exp. = very small #s (< 1) + Exp.= very large #s 2.7  10–3 0.0027

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #3 Translating Scientific Notation to Standard Notation Write the number in standard notation. 2.01  104 2.01  104 Think: Move the decimal right 4 places as positive exponent = very large #. 20,100

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #4 Translating Scientific Notation to Standard Notation Write the number in standard notation. 1.9  10–5 1.9  10 –5 Think: Move the decimal left 5 places as negative exponent = very small # . 0.000019

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #5 Translating Scientific Notation to Standard Notation Write the number in standard notation. 2.87  109 2.87  10 9 2,870,000,000 Think: Move the decimal right 9 places as positive exponent = very large #.

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #6 Translating Scientific Notation to Standard Notation Write the number in standard notation. 8.651  107 8.651  10 7 86, 510,000 Think: Move the decimal right 7 places as positive exponent = very large #.

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #7 Translating Scientific Notation to Standard Notation Write the number in standard notation. 7.3  10-6 7.3  10 -6 0.0000073 Think: Move the decimal right 6 places as positive exponent = very large #.

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #8 Translating Scientific Notation to Standard Notation Write the number in standard notation. 4.0027  10-4 4.0027  10 -4 Think: Move the decimal right 4 places as positive exponent = very large #. 0.00040027

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #9 Translating Scientific Notation to Standard Notation Write the number in standard notation. 5.2277  10-3 5.2277  10 -3 0.0052277 Think: Move the decimal right 3 places as positive exponent = very large #.

Translating Scientific Notation to Standard Notation Course 3 Scientific Notation #10 Translating Scientific Notation to Standard Notation Write the number in standard notation. 2.91  105 2.91  10 5 291,000 Think: Move the decimal right 5 places as positive exponent = very large #.

Now… let’s try the inverse… Now… let’s try the inverse….. Translating from scientific notation to standard notation

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #11 Translating Standard Notation to Scientific Notation Write 6,590 in scientific notation. 6,590 Think: The decimal needs to move 3 places to get a number between 1 and 10. 6.59 6.59  10 Set up scientific notation. Think: The number is very large so make exponent positive. written in scientific notation is 6.590  103.

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #12 Translating Standard Notation to Scientific Notation Write 0.00916 in scientific notation. 0.00916 To Scientific Notation: Move decimal point to right of first non-zero digit. Set up scientific notation. Exponent = # places you moved decimal point. *If very small #, use – exponent. *If very large #, use + exponent. 9.16 9.16  10 So 0.00916 written in scientific notation is 9.16  10–3.

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #12 Translating Standard Notation to Scientific Notation Write 0.00709 in scientific notation. 0.0121 To Scientific Notation: Move decimal point to right of first non-zero digit. Set up scientific notation. Exponent = # places you moved decimal point. *If very small #, use – exponent. *If very large #, use + exponent. So 0.0121 written in scientific notation is 1.21  10–2.

Course 3 Scientific Notation #141 Check It Out: Example 2 Write 0.000811 in scientific notation. Think: The decimal needs to move 4 places to get a number between 1 and 10. 0.000811 8.11 8.11  10 Set up scientific notation. Think: The number is very small so make exponent negative. So 0.000811 written in scientific notation is 8.11  10–4. Check 8.11  10 = 8.11  0.0001 = 0.000811 –4

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #151 Translating Standard Notation to Scientific Notation Write 225,000 in scientific notation. 225,000 Think: The decimal needs to move 5 places to get a number between 1 and 10. 2.25 2.25  10 Set up scientific notation. Think: The number is very large so make exponent positive. So 225,000 written in scientific notation is 2.25  105. Check 2.25  105 = 2.25  100,000 = 225,000

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #16 Translating Standard Notation to Scientific Notation Write 2,204,000,000 in scientific notation. Think: The decimal needs to move 5 places to get a number between 1 and 10. Set up scientific notation. Think: The number is very large so make exponent positive. So 2,204,000,000 written in scientific notation is 2.204  109.

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #17 Translating Standard Notation to Scientific Notation Write 429,000 in scientific notation. 429,000 Think: The decimal needs to move 5 places to get a number between 1 and 10. 4.29 4.29  10 Set up scientific notation. Think: The number is very large so make exponent positive. So 429.000 written in scientific notation is 4.29  105. Check 4.29  105 = 4.29  100,000 = 429,000

Translating Standard Notation to Scientific Notation Course 3 Scientific Notation #141 Translating Standard Notation to Scientific Notation Write 0.000407 in scientific notation. Think: The decimal needs to move 4 places to get a number between 1 and 10. 0.000407 Set up scientific notation. Think: The number is very small so make exponent negative. So 0.000407 written in scientific notation is 4.07  10–4. –4

Scientific Notation Ticket out the door : Course 3 Scientific Notation Ticket out the door : Write each number in standard notation. 1. 1.72  104 17,200 2. 6.9  10–3 0.0069 Write each number in scientific notation. 5.3  10–3 3. 0.0053 5.7  107 4. 57,000,000

4-4 Scientific Notation Lesson Quiz: Part II Course 3 4-4 Scientific Notation Lesson Quiz: Part II 6. A human body contains about 5.6  106 microliters of blood. Write this number in standard notation. 5,600,000

Multiplying in SN

Multiplication in Scientific Notation Course 3 4-4 Scientific Notation Multiplication in Scientific Notation The number 123,000,000,000 in scientific notation is: 1.23 x 1011 Rules for Multiplying in SN: 1.) Multiply the coefficients (decimal parts). 2.) Multiply the powers of 10. Keep the base of 10 & add the exponents. coefficient base (always 10 with exponent in SN)

Multiplication in Scientific Notation Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 1: (3.0 x 104)(2.0 x 105) 3.0 x 2.0 = 6.0 104 x 105 = 109 So . . . 6.0 x 109

Multiplication in Scientific Notation Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 2: What happens if the coefficient is more than 10? (5.0 x 103)(6.0 x 103) 5.0 x 6.0 = 30 103 x 103 = 106 So . . . 30 x 106 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10.

Multiplication in Scientific Notation Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 2 (cont.): What happens if the coefficient is more than 10? (5.0 x 103)(6.0 x 103) So . . . 30 x 106 Becomes . . . 3.0 x 107 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets smaller, exponent gets bigger.

Multiplication in Scientific Notation Course 3 4-4 Scientific Notation Multiplication in Scientific Notation Example 3: (2.2 x 104)(7.1 x 105) 2.2 x 7.1 = 15.62 104 x 105 = 109 So . . . 1.562 x 1010 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets smaller, exponent gets bigger.

Division in Scientific Notation Course 3 4-4 Scientific Notation Division in Scientific Notation The number 123,000,000,000 in scientific notation is: 1.23 x 1011 Rules for Dividing in SN: 1.) Divide the coefficients (decimal parts). 2.) Divide the powers of 10. Keep the base of 10 & subtract the exponents. coefficient base (always 10 with exponent in SN)

Division in Scientific Notation Course 3 4-4 Scientific Notation Division in Scientific Notation Example 1: (6.0 x 109) ÷ (2.0 x 105) 6.0 ÷ 2.0 = 3.0 109 ÷ 105 = 104 So . . . 3.0 x 104

Division in Scientific Notation Course 3 4-4 Scientific Notation Division in Scientific Notation Example 2: What happens if the coefficient is not between 1 and 10? (1.8 x 107) ÷ (6.0 x 103) 1.8 ÷ 6 = 0.3 107 ÷ 103 = 104 So . . . 0.3 x 104 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10.

Division in Scientific Notation Course 3 4-4 Scientific Notation Division in Scientific Notation Example 2 (cont.): What happens if the coefficient is not between 1 and 10? (1.8 x 107) ÷ (6.0 x 103) So . . . 0.3 x 104 Becomes . . . 3.0 x 103 Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets bigger, exponent gets smaller.

Division in Scientific Notation Course 3 4-4 Scientific Notation Division in Scientific Notation Example 3: (4.2 x 102) ÷ (7.0 x 105) 4.2 ÷ 7.0 = 0.6 102 ÷ 105 = 10-3 So . . . 0.6 x 10-3 becomes . . . Remember: When the product is not written correctly in SN, you must move the decimal until the coefficient is between 1 and 10. **When decimal part gets bigger, exponent gets smaller. 6.0 x 10-4

Additional Example: Application Course 3 4-4 Scientific Notation Additional Example: Application A pencil is 18.7 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters long would they be? Write the answer in scientific notation. 1 centimeter = 10 millimeters 18.7 centimeters = 187 millimeters Multiply by 10 to change from cm to mm. 187 mm  10,000 Find the total length. 1,870,000 mm Multiply.

Additional Example Continued Course 3 4-4 Scientific Notation Additional Example Continued 1.87  10 Set up scientific notation. Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive. Think: The decimal needs to move 6 places. In scientific notation the 10,000 pencils would be 1.87  106 mm long, laid end-to-end.

Additional Example 4: Life Science Application Course 3 4-4 Scientific Notation Additional Example 4: Life Science Application A certain cell has a diameter of approximately 4.11 x 10-5 meters. A second cell has a diameter of 1.5 x 10-5 meters. Which cell has a greater diameter? 4.11 x 10-5 1.5 x 10-5 10-5 = 10-5 Compare powers of 10. Compare the values between 1 and 10. 4.11 > 1.5 4.11 x 10-5 > 1.5 x 10-5 The first cell has a greater diameter.

4-4 Scientific Notation Check It Out: Example 4 Course 3 4-4 Scientific Notation Check It Out: Example 4 A certain cell has a diameter of approximately 5 x 10-3 meters. A second cell has a diameter of 5.11 x 10-3 meters. Which cell has a greater diameter? 5 x 10-3 5.11 x 10-3 10-3 = 10-3 Compare powers of 10. Compare the values between 1 and 10. 5 < 5.11 5 x 10-3 < 5.11 x 10-3 The second cell has a greater diameter.