3.1 Using and Expressing Measurements > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Scientific Notation & Significant Figures Notes

3.1 Using and Expressing Measurements > 2 measurement is a number and a unitA *measurement is a quantity that has both a number and a unit. Scientific Notation scientific notation = a coefficient x 10 n In scientific notation, a given number is written as the product of two numbers = a coefficient x 10 n *n = exponent Example: 602,000,000,000,000,000,000, x  6.02 x 10 23

3.1 Using and Expressing Measurements > 3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. If the coefficient > 10 Decimal moves to the left # spaces = n  + 6,300,000. = 94,700. = Scientific Notation If the coefficient < 1 Decimal moves to the right # spaces = n  = = 6.3 x x x x How to Write in Scientific Notation

3.1 Using and Expressing Measurements > 4 Practice Problems #1: Practice Problems #1: Write the following in scientific notation. ① 3,400 = ② 101,000 = ③ = ④ = ⑤ = ⑥ 1,000,000 = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. ***DO PRACTICE PROBLEMS ON THE BOARD***

3.1 Using and Expressing Measurements > 5 ***REMEMBER*** Move the decimal point until you have 1 WHOLE NUMBER to the LEFT OF DECIMAL POINT! Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

3.1 Using and Expressing Measurements > 6 To multiply: multiply the coefficients and add the n. (3 x 10 4 ) x (2 x 10 2 ) = (2.1 x 10 3 ) x (4.0 x 10 –7 ) = Scientific Notation Multiplication and Division To divide: divide the coefficients and subtract the n(numerator – denominator). 3.0 x x 10 2 = ( 6.0 ) x 10 5–2 = 0.5 x 10 3 (3 x 2) x = 6 x 10 6 (2.1 x 4.0) x 10 3+(–7) = 8.4 x 10 –4 3.0 = 5.0 x 10 2

3.1 Using and Expressing Measurements > 7 ① (8.0 x 10 –2 ) x (7.0 x 10 –5 ) = ② (6.6 x 10 6 )  (2.2 x 10 2 ) = ③ (5.0 x 10 6 )  (2.0 x 10 4 ) = ④ (3.0 x 10 –3 ) x (2.5 x 10 –4 ) = ⑤ (8.8 x 10 –2 ) x (2.5 x 10 3 ) = Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. ***DO PRACTICE PROBLEMS ON THE BOARD*** Practice Problems #2: Practice Problems #2: Solve the following problems and write your answers in scientific notation.

3.1 Using and Expressing Measurements > 8 *Significant Figures The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Significant Figures

3.1 Using and Expressing Measurements > 9 1.Every nonzero digit is significant m m 714 m 2.Zeros appearing between nonzero digits are significant m m m Significant Figures Rules of Significant Figures

3.1 Using and Expressing Measurements > 10 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3.All zeros on the left are not significant. To eliminate, write the number in scientific notation m = 7.1 x m 0.42 m = 4.2 x m m = 9.9 x m 4.To be significant, Zeros must be after a number and after the decimal point m m m Significant Figures Determining Significant Figures in Measurements

3.1 Using and Expressing Measurements > 11 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5.Zeros in front of the decimal point are not significant. 300 m 7000 m 27,210 m If zeros were exact measurements, then they’re significant. Write the value in scientific notation. 300 m = Significant Figures Determining Significant Figures in Measurements 3.00 x 10 2 m

3.1 Using and Expressing Measurements > 12 ① g  ② 2500 m  ③ kg  ④ g  ⑤ 28.0 ml  ⑥ g  Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Practice Problems #3: Practice Problems #3: Determine the number of sig figs. ***DO PRACTICE PROBLEMS ON THE BOARD***

3.1 Using and Expressing Measurements > 13 Rounding decide how many significant figures1. decide how many significant figures round to that many digits2. round to that many digits Note: If the next number is <5, digit stays the same. If the next number is ≥5, round up. For Example: a m (four)  b m (two)  c.8792 m (two)  Significant Figures Significant Figures in Calculations m 1.8 x m 8.8 x 10 3 m x 10 2 m

3.1 Using and Expressing Measurements > 14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Multiplication and Division Round the answer to the same number of significant figures as the measurement with the least number of significant figures.Round the answer to the same number of significant figures as the measurement with the least number of significant figures m x 0.34 m = m 2 = 2.6 m 2 = 2.6 m 2 Significant Figures Significant Figures in Calculations

3.1 Using and Expressing Measurements > 15 ① 2.10 m x 0.70 m ② m 2  m ③ m 2  8.4 m ④ 8.3 m x 2.22 m Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. ***DO PRACTICE PROBLEMS ON THE BOARD*** Practice Problems #4: Practice Problems #4: Solve the following problems. Write the answers in the correct number of sig figs and in scientific notation.