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Lesson 10.7 Operations in Scientific Notations

DAY 1

Watch the videos to take notes- multiplying scientific notations https://www.bigideasmath.com/protected/content/dcs_cc2/tutorials /mp4/cc12/grade%208/chapter%209/section%206/ltut_8_09_06_4/l tut_8_09_06_4.html

Multiplying Numbers in Scientific Notation: Rewrite the problem by grouping the factors together and then the powers together. Multiply the factors. Then multiply the powers of 10 by adding the exponents. Write in scientific notation. Make sure the factor is greater than 1 and less than 10.

Example 1:(3.42 x 105)(4.67 x 109) Multiply decimals: (3.42)(4.67) = 15.97 Add Exponents: 105∙109 =105+9 =1014 15.97 x 1014 15.97 = 1.597 x 101 (1.597 x 101)(1014) Rewrite in Scientific Notation if needed. Final Answer: 1.597 X 1015

Example 2: (2.93 x 10-2)(8.3 x 10-5) Multiply Decimals: (2.93)(8.3) = 24.319 Add Exponents: 10-2 ∙10-5 =10-2+(-5) =10-7 24.319 x 10-7 24.319 = 2.4319 x 101 (2.4319 x 101)(10-7) Rewrite in Scientific Notation Final Answer: 2.43 X 10-6

DAY 2

Warm-Up #6 Simplify 1. 36 12 ∙ 10 4 10 −3 2. 28 7 ∙ 10 8 10 3 3. 𝑏 4 ∙ 𝑏 6 𝑏 12

Homework Worksheet: Lesson 10.7B Hw

watch and take notes https://www. bigideasmath watch and take notes https://www.bigideasmath.com/protected/content/dcs_cc2/tutorials/ mp4/cc12/grade%208/chapter%209/section%206b/ltut_8_09_06b_3/l tut_8_09_06b_3.html Watch and don’t have to take notes https://www.youtube.com/watch?v=UADVIDjdaVg&t=336s

Dividing Numbers in Scientific Notation: Rewrite the problem by grouping the factors together and then the powers together. Divide the factors. Then divide the powers of 10 by subtracting the exponents. Write in scientific notation. Make sure the coefficient is greater than 1 and less than 10.

Example 1: 28 x 10 −3 2 x 10 −2 Divide decimals: 28÷2 = 14 Subtract exponents: (-3) – (-2)= -1 14 x 10 −1 14 = 1.4 x 10 1 (1.4 x 10 1 )( 10 −1 ) Final Answer: 𝟏.𝟒 𝐱 𝟏𝟎 𝟎 or 1.4

Example 2: 3.45 x 10 2 1.23 x 10 −5 Divide decimals: 3.45 ÷ 1.23= 2.81 Subtract exponents: 2 – (-5) =7 Answer: 2.81 X 107

DAY 3

Watch the video before taking notes https://www.youtube.com/watch?v=p0zVNTko7z4&t=360s

Adding Subtracting Numbers in Scientific Notation: When adding or subtracting numbers in scientific notation, the exponents must be the same. If it is not the same exponents then you need to change one exponent to match the other one. Line up the decimals to add or subtract. Write in scientific notation. Make sure the coefficient is greater than 1 and less than 10.

Example 1: Adding With the Same Exponents (3.45 x 103) + (6.11 x 103) 3.45 + 6.11 = 9.56 check to make sure the answer is in scientific notation 9.56 x 103

Example 2: Subtracting With the Same Exponents (8.96 x 107) – (3.41 x 107) 8.96 – 3.41 = 5.55 check to make sure the answer is in scientific notation 5.55 x 107

Example 3: (2.46 x 106) + (3.4 x 103) Step 1 – Rewrite with the same exponents 3.4 x 103  0.0034 x 103+3 (2.46 x 106) + (0.0034 x 106) Step 2 – Add decimals 2.46 + 0.0034 = 2.4634 Step 3 – Bring Down Exponents 2.4634 x 106

Example 4:(5.762 x 103) – (2.65 x 10-1) Step 1 – Rewrite with the same exponents 2.65 x 10-1  0.000265 x 10(-1+4) (5.762 x 103) – (0.000265 x 103) Step 2 – Subtract Decimals 5.762 – 0.000265 = 5.762 Step 3 – Bring down decimals 5.762 x 103

Example 5: (4.12 x 106) + (3.94 x 104) 4.12 x 106 = 412 x 104 (412 x 104) + (3.94 x 104) 412 + 3.94 = 415.94 415.94 x 104 415.94 = 4.1594 x 102 (4.1594 x 102) (104) Express in proper form: 4.15 x 106

Example 6: (4.23 x 103) – (9.56 x 102) (42.3 x 102) – (9.56 x 102) 42.3 – 9.56 = 32.74 32.74 x 102 32.74= 3.274 x 101 (3.274 x 101) (102) Express in proper form: 3.27 x 103