Operations with Scientific Notation (Part I, II, III, IV) 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(s): Using Math Principle, how can I add, subtract, multiply, and divide using scientific notation? Explain how do I use a scientific or graphing calculator to solve scientific notation problems?

Adding and Subtracting in Scientific Notation Part I

Addition and Subtraction with Scientific Notation Rules for adding and subtracting exponents are different from the properties of exponents. When adding and subtracting in scientific notation, the base 10 exponent must have like terms. (two of the base numbers will have same powers) Adding and subtracting in scientific notation can be done in scientific notation form or rewriting them in standard form.

Adding in Scientific Notation Method 1 Steps Simplify: (3.5 x 104) + (1.65 x 104) Step 1: 3.5 + 1.65 = 5.15 Step 1 – Add the terminating decimals. (3.5 + 1.65) Step 2: 104 are like terms Step 2 – Notice the base/exponents are like terms Step 3: 5.15 x 104 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.

Adding in Scientific Notation Method 2 Simplify: (7.5 x 105) + (5.20 x 103) Steps Step 1: 750,000 + 5,200 = Step 1 – Change the scientific notations to standard form. Why? Step 2: 755,200 Step 2 – Add them together to get the total number. Step 3: 7.552 x 105 Step 3 – Rewrite 755.200 in scientific notation form. Note: Always check to see if the decimals following the S.N rule.

Subtracting in Scientific Notation Method 1 and 2 Simplify: (8.5 x 105) - (5.2 x 105) Simplify: (3.5 x 104) - (1.2 x 102) Step 1: Change scientific notation to standard form Step 1: 8.5 – 5.2 = 3.3 Step 2 : 105 are like terms Step 2 : 35000 – 120 = 34880 Step 3: 3.3 x 105 Step 3: 3.488 x 104

Scientific Notation with Calculator Part II

Scientific Notation with Calculator Your can enter numbers in scientific notation by using a scientific calculator or graphing calculator (TI.83/84). Numbers/answers can be displayed in scientific notation form or standard form. On the TI-83 or TI 84, you will have to type terminating decimal, press the 2nd button, and EE button (comma button). The letter “E” will be shown on the display screen which takes the place of the base 10, and follow by the power. Example 1: 4.5E9 = 4.5 x 109

Scientific Notation with Calculator 2.94 x 1015 2.) 5.5E-11 = 5.5 x 10-11

Multiplying in Scientific Notation Part III

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. 1.) 1.452 x 1010 2. 2.) 3.664 x 103 3. 3.) 1.196 x 10-6 4. 4.) 3.9537

Dividing in Scientific Notation Part IV

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 adding, subtracting, multiplying or dividing numbers in scientific notation? What are some important things to remember when typing/reading scientific notation 0n a graphing calculator? Do you have clear understanding on how to multiply or divide in scientific notation? Explain Are there any more questions you may have using operations in scientific notation?