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.

Complete #1 & #2 on the scientific notation handout. Do Now: Complete #1 & #2 on the scientific notation handout. List 3 things you need to remember when writing values in scientific notation 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.

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 1 2 3 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Significant Figures 1 2 3 4 1 2 3 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

On a scaled instrument, estimate one more figure than you can actually read from the scale! Measurement = 2.5 inches 1 2 3 4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

If your measurement is “right on the line” the estimated figure is a “0”. Measurement = 3.0 inches 1 2 3 4 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.

Calculate percent error . Do Now: The boiling point of pure water is measured to be 99.1 deg C. The accepted boiling point for pure water is 100 deg C. Calculate error Calculate 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.

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

Accuracy, Precision, and Error Solubility of NaCl in 100 g Water Trial 1 Trial 2 Trial 3 Rhea 35.4 g 36.1 g 35.7 g Matt 31.8 g 34.1 g 41.5 g Shivani 39.2 g 39.3 g 38.9 g The correct value is 35.9 g Who is accurate & precise? Who is precise? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the difference between Scientific Notation What is the difference between 8 cm 8.0 cm 8.00 cm 8.000 cm 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.

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.

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.

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.

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.

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 Calculations Addition and Subtraction Round to the same number of decimal places (not digits) as the measurement with the least number of decimal places. a. 349.0 meters b. 74.626 meters 12.52 meters -28.34 meters + 8.24 meters 46.286 meters 369.76 meters 46.29 meters 369.8 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. 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 meters d. 0.365 meter2 ÷ 0.0200 meter = 18.3 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.