3.1 Measurements and Their Uncertainty Using and Expressing Measurements - A measurement is a quantity that has both a number and a unit. Scientific Notation - In chemistry you will encounter very large or very small numbers. Examples: 1 gram of hydrogen has 602,000,000,000,000,000,000,000 atoms 1 atom of gold has a mass of grams - These numbers can be more easily written as… x atoms 3.27 x grams

3.1 Measurements and Their Uncertainty Accuracy, Precision, and Error - Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. - Precision is a measure of how close a series of measurements are to one another.

3.1 Measurements and Their Uncertainty Determining Error - Accepted value: the correct value based on reliable references. - Experimental value: the value measured in the lab. Error = accepted value – experimental value Percent Error = (error / accepted value) x 100

3.1 Measurements and Their Uncertainty Significant Figures in Measurements - All properly taken measurements should be represented by a number with certain and uncertain digits. Measured length = 1.93 cm certain uncertain

3.1 Measurements and Their Uncertainty Significant Figures in Measurements Determine the correct number for each measurement..

3.1 Measurements and Their Uncertainty Significant Figures in Measurements. Ruler 1 is considered to be more precise. Measurement for Ruler #1: Object A = 6.79 cm Object B = 4.48 cm Measurement for Ruler #2: Object A = 6.8 cm Object B = 4.4 cm

3.1 Measurements and Their Uncertainty Rules for determining whether a digit in a measured value is significant: 250 marbles (Unlimited) 3 ft = 1 yd (Unlimited) 250 yards (2 sig. figs.) 4.58 feet (3 sig. figs.) yards (2 sig. figs.) 70,009 inches ________ 50,000 miles _________ degrees________ cm_________ 5 1 5

3.1 Measurements and Their Uncertainty Significant Figures in Calculations * In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. Rounding Round of each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation. a meters (four)Answer: b meter (two)Answer: c.8792 meters (two)Answer: x 10 2 meters 1.8 x meter 8.8 x 10 3 meters

3.1 Measurements and Their Uncertainty Significant Figures in Calculations Addition and Subtraction * The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. AdditionSubtraction

3.1 Measurements and Their Uncertainty Significant Figures in Calculations Multiplication and Division Answers to multiplication and division problems need to be rounded to the same number of significant figures as the measurement with the least number of significant figures. Multiplication Division