Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Write the following in scientific notation 238,900 0.000365 Do Now: Write the following in scientific notation 238,900 0.000365 Solve each problem. Answer in scientific notation. (4.5 x 104) + (6.3 x 103) (4.5 x 104) - (6.3 x 103) (4.5 x 104) x (6.3 x 103) (4.5 x 104) ÷ (6.3 x 103) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Coefficient x 10 exponent Scientific Notation Scientific notation: a number is written as the product of two numbers Coefficient x 10 exponent 602,000,000,000,000,000,000,000 = 6.02 x 1023 Coefficient: 6.02 Exponent: 23 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Scientific Notation The coefficient is always a number greater than or equal to one and less than ten. 60.2 x 1022 6.02 x 1023 602 x 1021 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Multiply the coefficients and add the exponents. Scientific Notation Multiplication Multiply the coefficients and add the exponents. (3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106 (2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Scientific Notation Division Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator. 3.0 x 105 3.0 ( ) = x 105–2 = 0.5 x 103 = 5.0 x 102 6.0 x 102 6.0 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Addition and Subtraction Scientific Notation Addition and Subtraction If you are not using a calculator, then the exponents must be the same (the decimal points must be aligned). (5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103) = (5.4 + 0.80) x 103 = 6.2 x 103 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Using Scientific Notation Sample Problem 3.1 Using Scientific Notation Solve each problem and express the answer in scientific notation. a. (8.0 x 10–2) x (7.0 x 10–5) b. (7.1 x 10–2) + (5 x 10–3) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Using Scientific Notation Sample Problem 3.1 Using Scientific Notation Solve each problem and express the answer in scientific notation. a. (8.0 x 10–2) x (7.0 x 10–5) b. (7.1 x 10–2) + (5 x 10–3) = 5.6 x 10–6 = 7.6 x 10–2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Measure the length and width of an index card using a ruler. Calculate the area of the index card. Width Length Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Measurement: quantity that has both a number and a unit. Examples Height: 66 inches Age: 15 years Body temperature: 37°C Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Any digit that gives us useful information is significant!!! Significant Figures Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Any digit that gives us useful information is significant!!! Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Accuracy, Precision, and Error Determining Error Experimental value: value measured in the lab. Accepted value: correct value for the measurement based on reliable references Error = experimental value – accepted value vaue Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Accuracy, Precision, and Error Determining Error Percent error: the absolute value of the error divided by the accepted value, multiplied by 100. Percent error = error accepted value 100 x Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating Percent Error Sample Problem 3.2 Calculating Percent Error The boiling point of pure water is measured to be 99.1°C. Calculate the percent error. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

|experimental value – accepted value| _______________________________ Sample Problem 3.2 Percent error = |experimental value – accepted value| _______________________________ accepted value X 100 |99.1°C – 100.0°C| X 100 = 100.0°C _______ = 100.0°C X 100 = 0.9% 0.9°C Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Do Now: What is the difference between the measurements 3 cm, 3.0 cm, and 3.00cm? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Accuracy, Precision, and Error Accuracy: a measure of how close a measurement comes to the actual or true value of whatever is measured. Precision: a measure of how close a series of measurements are to one another, irrespective of the actual value. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atlantic – Pacific Rule Significant Figures Atlantic – Pacific Rule Is there a decimal? Pacific Atlantic (Present) (Absent) Start from LEFT Start from RIGHT & count all #’s & count all #’s from first nonzero from first nonzero Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Determining Significant Figures Measurements - Use Atlantic – Pacific Rule Count – Infinite number of sig figs Defined quantities – Infinite number of sig figs Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Counting Significant Figures in Measurements Sample Problem 3.3 Counting Significant Figures in Measurements How many significant figures are in each measurement? 123 m 40,506 mm 9.8000 x 104 m 22 metersticks 0.070 80 m 98,000 m Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Counting Significant Figures in Measurements Sample Problem 3.3 Counting Significant Figures in Measurements How many significant figures are in each measurement? 123 m 3 sig figs 40,506 mm 5 sig figs 9.8000 x 104 m 5 sig figs 22 metersticks infinite 0.070 80 m 4 sig figs 98,000 m 2 sig figs Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Calculations Calculated answers CANNOT be more precise than the least precise measurement from which it was calculated. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Calculations Addition and Subtraction Round to the same number of decimal places (not digits) as the measurement with the least number of decimal places. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Addition and Subtraction Sample Problem 3.5 Significant Figures in Addition and Subtraction Perform the following calculation. Give each answer to the correct number of significant figures. a. 12.52 meters + 349.0 meters + 8.24 meters b. 74.626 meters – 28.34 meters Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Addition and Subtraction Sample Problem 3.5 Significant Figures in Addition and Subtraction Perform the following addition and subtraction operations. Give each answer to the correct number of significant figures. a. 12.52 meters + 349.0 meters + 8.24 meters b. 74.626 meters – 28.34 meters = 369.8 meters = 46.29 meters Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Calculations Multiplication and Division Round answer to the same number of significant figures as the measurement with the LEAST number of significant figures. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Multiplication and Division Sample Problem 3.6 Significant Figures in Multiplication and Division Perform the following operations. Give the answers to the correct number of significant figures. a. 7.55 meters x 0.34 meter b. 2.10 meters x 0.70 meter c. 2.4526 meters2 ÷ 8.4 meters d. 0.365 meter2 ÷ 0.0200 meter Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures in Multiplication and Division Sample Problem 3.6 Significant Figures in Multiplication and Division Perform the following operations. Give the answers to the correct number of significant figures. a. 7.55 meters x 0.34 meter = 2.6 meters2 b. 2.10 meters x 0.70 meter = 1.5 meters2 c. 2.4526 meters2 ÷ 8.4 meters = 0.29 meter d. 0.365 meter2 ÷ 0.0200 meter = 18.3 meters Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 3.4 Do Now: Round each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation. a. 314.721 meters (four) b. 0.001 775 meter (two) c. 8792 meters (two) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 3.4 Do Now: Round each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation. a. 3.147 x 102 meters b. 1.8 x 10-3 meter c. 8.8 x 103 meters Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

END OF 3.1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.