1. Be able to carry out basic mathematical operations using numbers expressed in scientific notation, without changing them to decimal notation. Be able to carry out basic mathematical operations using numbers expressed in scientific notation, without changing them to decimal notation. 1 Section 2.8 Mathematical Operations in Scientific Notation Student Learning Focus

2. Multiplying and Dividing in scientific notation is pretty straightforward. Multiplying and Dividing in scientific notation is pretty straightforward. Fewest number of significant figures in the coefficient. Fewest number of significant figures in the coefficient. 2 Section 2.8 Mathematical Operations in Scientific Notation Multiplication and Division in Scientific Notation

3. (2.05 x 10 –3 ) x (1.19 x 10 –7 ) (2.05 x 10 –3 ) x (1.19 x 10 –7 ) Calculator gives 2.4395 x 10 –10 Calculator gives 2.4395 x 10 –10 But this answer has 5 sig figs in the coefficient But this answer has 5 sig figs in the coefficient Your calculator does not know about sig figs Your calculator does not know about sig figs The actual answer is 2.44 x 10 –10 The actual answer is 2.44 x 10 –10 3 Section 2.8 Mathematical Operations in Scientific Notation Multiplication and Division in Scientific Notation

4. Solve the following and express the answer in scientific notation to the correct number of significant figures. 1.(2.340 x 10 –3 ) x (2.60 x 10 6 ) 1.(8.77 x 10 –6 ) x (7.00 x 10 –2 ) 4 Section 2.7 Expressing Numbers in Scientific Notation Learning Check

5. Solve the following and express the answer in scientific notation to the correct number of significant figures. 1.(2.340 x 10 –3 ) x (2.60 x 10 6 ) 6084 = 6.08x10 3 2.(8.77 x 10 –6 ) x (7.00 x 10 –2 ) 0.0000006.14 = 6.14x10 –7 5 Section 2.7 Expressing Numbers in Scientific Notation Solution

6. Addition and Subtraction in Scientific Notation is a little trickier. Addition and Subtraction in Scientific Notation is a little trickier. Remember the rule for significant figures for addition and subtraction is that the least precise number sets the limit on the sig figs Remember the rule for significant figures for addition and subtraction is that the least precise number sets the limit on the sig figs When the exponents are different it is hard to tell which number is the least precise. When the exponents are different it is hard to tell which number is the least precise. 6 Section 2.8 Mathematical Operations in Scientific Notation Addition and Subtraction in Scientific Notation

7. 1.25 x 10 –3 + 6.33 x 10 –5 1.25 x 10 –3 + 6.33 x 10 –5 There are two ways to deal with this There are two ways to deal with this 1. Equalize the exponents 1. Equalize the exponents 2. Determine the uncertainty for each number and use the most uncertain (least precise) 2. Determine the uncertainty for each number and use the most uncertain (least precise) 7 Section 2.8 Mathematical Operations in Scientific Notation Addition and Subtraction in Scientific Notation

8. 1.25 x 10 –3 + 6.33 x 10 –5 1.25 x 10 –3 + 6.33 x 10 –5 Equalize the exponents (always use the larger exponent) Equalize the exponents (always use the larger exponent) 1.25 x 10 –3 1.25 x 10 –3 0.0633 x 10 –3 0.0633 x 10 –3 When the coefficients are added the lease precise value is 1.25 so the answer can only be precise to the 100ths place When the coefficients are added the lease precise value is 1.25 so the answer can only be precise to the 100ths place 1.25 + 0.0633 = 1.3133 = 1.31 x 10 –3 1.25 + 0.0633 = 1.3133 = 1.31 x 10 –3 8 Section 2.8 Mathematical Operations in Scientific Notation Addition and Subtraction in Scientific Notation

9. 1.25 x 10 –3 + 6.33 x 10 –5 1.25 x 10 –3 + 6.33 x 10 –5 Determine the uncertainty for each number and use the number with the larger uncertainty Determine the uncertainty for each number and use the number with the larger uncertainty 1.25 x 10 –3 10 –2 x 10 –3 = 10 –5 larger uncertainty 1.25 x 10 –3 10 –2 x 10 –3 = 10 –5 larger uncertainty 6.33 x 10 –5 10 –2 x 10 –5 = 10 –7 6.33 x 10 –5 10 –2 x 10 –5 = 10 –7 The answer must have the same uncertainty –5 The answer must have the same uncertainty –5 0.0013133= 1.31 x 10 –3 10 –2 x 10 –3 = 10 –5 0.0013133= 1.31 x 10 –3 10 –2 x 10 –3 = 10 –5 9 Section 2.8 Mathematical Operations in Scientific Notation Addition and Subtraction in Scientific Notation

10. Solve the following and express the answer in scientific notation to the correct number of significant figures. 1.(7.431 x 10 8 ) + (4.00 x 10 6 ) 1.(7.431 x 10 –8 ) – (4.00 x 10 –3 ) 10 Section 2.8 Mathematical Operations in Scientific Notation Learning Check

11. Solve the following and express the answer in scientific notation to the correct number of significant figures. (7.431 x 10 8 ) + (4.00 x 10 6 ) Equalize the exponents 7.431x 10 8 + 0.0400 x 10 8 7.4710x10 6 7.471x10 8 11 Section 2.8 Mathematical Operations in Scientific Notation Solution

12. Solve the following and express the answer in scientific notation to the correct number of significant figures. (7.431 x 10 8 ) + (4.00 x 10 6 ) Determine the uncertainty for each number and use the larger uncertainty 7.431 x 10 8 10 –3 x 10 8 = 10 5 larger uncertainty 4.00 x 10 6 10 –2 x 10 6 = 10 4 The answer must have the same uncertainty 10 4 7.471 x 10 8 10 –3 x 10 8 = 10 5 12 Section 2.8 Mathematical Operations in Scientific Notation Solution

13. Solve the following and express the answer in scientific notation to the correct number of significant figures (7.431 x 10 –8 ) – (4.00 x 10 –3 ) Calculator answer 3.999992569 x 10 – 3 Equalize the exponents 0.00007431 x 10 –3 – 4.00 x 10 –3 – 4.00 x 10 –3 13 Section 2.8 Mathematical Operations in Scientific Notation Solution

14. Solve the following and express the answer in scientific notation to the correct number of significant figures. (7.431 x 10 –8 ) – (4.00 x 10 –3 ) Determine the uncertainty for each number and use the larger uncertainty 7.431 x 10 –8 10 –3 x 10 –8 = 10 –11 4.00 x 10 –3 10 –2 x 10 –3 = 10 –5 larger uncertainty Calculator answer 3.999992569 x 10 – 3 The answer must have the same uncertainty – 5 – 4.00 x 10 –3 14 Section 2.8 Mathematical Operations in Scientific Notation Solution