Multiplying and Dividing Using Scientific Notation 8 th

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

Goal/Standards • 8. EE. 4 – Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both decimal and scientific notation are used.

Essential Question: How can I use the law of exponents to help me multiply and divide numbers in scientific notation?

Target Statement: ØI CAN use the law of exponents to help me multiply and divide numbers/decimals in scientific notation.

Scientific Notation with Online Scientific Calculator • You can enter numbers in scientific notation by using a scientific calculator • Numbers/answers can be displayed in scientific notation form or standard form. • Scientific Calculator can be found on https: //www. desmos. com/scientific

Scientific Calculator

Scientific Notation with Calculator 1. ) Type 4. 5 x 104 = 45000 2. ) Type. 000013; click on 1. 3 x 10 -5

Multiplying in Scientific Notation Part I

Properties of Exponents 1. When multiplying or dividing numbers written in scientific notation, you can use the properties of exponents to help get the answer. The following are properties we will use: a. Multiplication Property of Exponents When multiplying bases with exponents, you add the exponents. b. Dividing Property of Exponents When dividing bases with exponents, you subtract the exponents.

Multiplying in Scientific Notation Example # 1 Simplify: (2. 5 Steps x 104) (3. 4 x 102) Step 1: 2. 5 x 3. 4 = 8. 5 4 2 6 Step 2: 10 x 10 = 10 Step 3: 8. 5 x 106 Step 1 – Multiply the terminating decimals. (2. 5 x 3. 4) Step 2 – Add the exponents of 104 and 102 Step 3 – Rewrite step 1 and step 2 in scientific notation form. Always check to see if the decimals following the S. N rule. Note:

Multiplying in Scientific Notation Example # 2 Simplify: (4. 2 x 109) (5. 5 x 102) Step 1: 4. 2 x 5. 5 = 23. 1 9 2 11 Step 2: 10 x 10 = 10 11 Step 3: 23. 1 x 10 Step 4: 2. 31 x 1012 Is this answer in S. N form? Explain Steps Step 1 – Multiply the terminating decimals. (4. 2 x 5. 5 ) Step 2 – Add the exponents of 109 and 102 Step 3 – Rewrite step 1 and step 2 in scientific notation form. 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

Multiplying in Scientific Notation Example # 3 Simplify: (7. 4 x 10 -3) (2. 5 x 10 -3) Step 1: 7. 4 x 2. 5 = 18. 5 -3 -3 -6 Step 2: 10 x 10 = 10 Step 3: 18. 5 x 10 -6 Step 4: 1. 85 x 10 -5 Is this answer in S. N. form? Explain Steps Step 1 : Multiply the terminating decimals. (7. 4 x 2. 5 ) Step 2 : Add the exponents of 10 -3 and 10 -3 Step 3 : Rewrite step 1 and step 2 in scientific notation form. 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

Dividing in Scientific Notation Part II

Dividing in Scientific Notation Example # 4 Steps Simplify: Step 3: 2 x 102 Step 2 – Subtract the exponents of 103 and 101 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.

Dividing in Scientific Notation Example # 5 Simplify: Step 3: 2. 43 x 10 -1 Steps Step 2 – Subtract the exponents of 104 and 105 ( 4 – 5 = -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.

Dividing in Scientific Notation Example # 6 Simplify: Steps Step 2 – Subtract the exponents of 10 -6 and 105 (-6 - 5= -11) Step 3: 0. 822 x 10 -11 Is this answer in S. N. form? Explain Step 4: 8. 22 x 10 -12 Step 3 – Rewrite step 1 and step 2 in scientific notation form. 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

Dividing in Scientific Notation Example # 7 Simplify: Steps Step 3: 3. 103 x 102 Step 2 – Subtract the exponents of 10 -4 and 10 -6 [-4 – (-6) = -4 + 6 = 2] Step 3 – Rewrite step 1 and step 2 in scientific notation form. Check to see if it is in the correct form.

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

Dividing in Scientific Notation Practice 5. 6. 7. 8.

Summary 1. What are some important strategies you should remember when adding, subtracting, multiplying or dividing numbers in scientific notation? 2. Can you complete the two target statements. 3. What are some important things to remember when typing/reading scientific notation 0 n a graphing calculator? 4. Do you have clear understanding on how to multiply or divide in scientific notation? Explain 5. Are there any more questions you may have using operations in scientific notation?