Scientific Notation Part II Multiplying and Dividing 8th Grade Math By Mr. Laws

Goal/Standards 8.EE.4 – Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation is used. Interpret scientific notation that has been generated by technology.

Essential Question: Using Math Principle, how can I use the properties of exponents to multiply or divide numbers written in scientific notation?

Properties of Exponents When multiplying or dividing numbers written in scientific notation, when can use the properties of exponents to help get the answer. The following are properties we will use: Multiplication Property of Exponents When multiplying bases with exponents, you add the exponents. Dividing Property of Exponents When dividing bases with exponents, you subtract the exponents.

Multiplying in Scientific Notation Example # 1 Steps Simplify: (2.5 x 104) (3.4 x 102) Step 1: 2.5 x 3.4 = 8.5 Step 1 – Multiply the terminating decimals. (2.5 x 3.4) Step 2: 104 x 102 = 106 Step 2 – Add the exponents of 104 and 102 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Note: Always check to see if the decimals following the S.N rule. Step 3: 8.5 x 106

Multiplying in Scientific Notation Example # 2 Steps Simplify: (4.2 x 109) (5.5 x 102) Step 1: 4.2 x 5.5 = 23.1 Step 1 – Multiply the terminating decimals. (4.2 x 5.5 ) Step 2: 109 x 102 = 1011 Step 2 – Add the exponents of 109 and 102 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Is this answer in S.N form? Explain Step 3: 23.1 x 1011 Step 4– Change 23.1 to 2.31 by moving decimal point one place to the left, and add 1 exponent to 1011 to make it 1012 Step 4: 2.31 x 1012

Multiplying in Scientific Notation Example # 3 Steps Simplify: (7.4 x 10-3) (2.5 x 10-3) Step 1: 7.4 x 2.5 = 18.5 Step 1 : Multiply the terminating decimals. (7.4 x 2.5 ) Step 2: 10-3 x 10-3 = 10-6 Step 2 : Add the exponents of 10-3 and 10-3 Step 3 : Rewrite step 1 and step 2 in scientific notation form. Is this answer in S.N. form? Explain Step 3: 18.5 x 10-6 Step 4: Change 18.5 to 1.85 by moving decimal point one place to the left, and add 1 to 10-6 to make it 10-5 Step 4: 1.85 x 10-5

Multiplying in Scientific Notation Practice 1. 2. 3. 4.

Dividing in Scientific Notation Example # 4 𝟒.𝟐 𝒙 𝟏𝟎 𝟑 𝟐.𝟏 𝒙 𝟏𝟎 𝟏 Steps Simplify: Step 1 – Divide the terminating decimals. (4.2 ÷ 2.1) Step 1: 4.2 ÷ 2.1 = 2 Step 2 – Subtract the exponents of 103 and 101 Step 2: 103 ÷ 101 =102 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Note: Always check to see if the decimals following the S.N rule. Step 3: 2 x 102

Dividing in Scientific Notation Example # 5 𝟔.𝟗 𝒙 𝟏𝟎 𝟒 𝟐.𝟖𝟒 𝒙 𝟏𝟎 𝟓 Steps Simplify: Step 1 – Divide the terminating decimals. (6.9 ÷ 2.84) Step 1: 6.9 ÷ 2.84 = 2.43 Step 2 – Subtract the exponents of 104 and 105 ( 4 – 5 = -1) Step 2: 104 ÷ 105 =10-1 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Note: Always check to see if the decimals following the S.N rule. Step 3: 2.43 x 10-1

Dividing in Scientific Notation Example # 6 𝟓.𝟏 𝒙 𝟏𝟎 −𝟔 𝟔.𝟐 𝒙 𝟏𝟎 𝟓 Steps Simplify: Step 1 – Divide the terminating decimals. (5.1 ÷ 6.2) Step 1: 5.𝟏÷ 6.2 = 0.822 Step 2 – Subtract the exponents of 10-6 and 105 (-6 - 5= -11) Step 2: 10-6 ÷ 105 =10-11 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Step 3: 0.822 x 10-11 Is this answer in S.N. form? Explain Step 4: Change 0.822 to 8.22 by moving decimal point one place to the right, and add -1 exponent to 10-11 to make it 10-12 Step 4: 8.22 x 10-12

Dividing in Scientific Notation Example # 7 𝟗 𝒙 𝟏𝟎 −𝟒 𝟐.𝟗 𝒙 𝟏𝟎 −𝟔 Steps Simplify: Step 1 – Divide the terminating decimals. (9 ÷ 2.9) Step 1: 9 ÷ 2.9 = 3.103 Step 2 – Subtract the exponents of 10-4 and 10-6 [-4 – (-6) = -4 + 6 = 2] Step 2: 10-4 ÷ 10-6 =102 Step 3: 3.103 x 102 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Check to see if it is in the correct form.

Dividing in Scientific Notation Practice 1. 2. 3. 4.

Summary What are some important strategies you should remember when multiplying or dividing numbers in scientific notation? Do you have clear understanding on how to multiply or divide in scientific notation? Explain Are there any more questions you may have about multiplying and dividing in scientific notation?