Using and Expressing Measurements 3.1 Using and Expressing Measurements Using and Expressing Measurements How do measurements relate to science?

Using and Expressing Measurements 3.1 Using and Expressing Measurements A measurement is a quantity that has both a number and a unit. it is important to be able to make measurements and to decide whether a measurement is correct.

Scientific Notation http://www.youtube.com/watch?v=H578q UeoBC0 Scientific Notation Pre-Test

Scientific Notation 210, 000,000,000,000,000,000,000 This number is written in decimal notation. When numbers get this large, it is easier to write it in scientific notation Where is the decimal in this number?

210, 000,000,000,000,000,000,000. Decimal needs moved to the left between the 2 and the 1 ( numbers that are between 1-10) When the original number is more than 1 the exponent will be positive. 2.1 x 1023 Exponents show how many places decimal was moved

Express 4.58 x 106 in decimal notation Remember the exponent tells you how many places to move the decimal. The exponent is positive so the decimal is moved to the right 4,580, 000

express the number 0. 000000345 in scientific notation express the number 0.000000345 in scientific notation. Decimal moved between first 2 non-zero digits and will be moved 7 times 3.45 x 10 -7 The exponent is negative because the original number is a very small number

Express the following in scientific notation or standard notation 1. 74171.7 2. .07882 3. 526 4. .0000573 5. 5.8 x 10 -7 6. 5.256 x 106

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error Accuracy, Precision, and Error What is the difference between accuracy and precision?

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error Accuracy and Precision 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.

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error Determining Error The accepted (Known) value is the correct value based on reliable references. The experimental value is the value measured in the lab. The difference between the experimental value and the accepted value is called the error.

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%. Experimental – known Expressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error Percent Error (Error) 3.00-measurement X 100 3.00

Accuracy, Precision, and Error 3.1 Accuracy, Precision, and Error Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. There is a difference between the person’s correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the person’s actual weight is 107 lb?

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% ERROR The density of aluminum is known to be 2.7 g/ml. In the lab you calculated the density of aluminum to be 2.4 g/ml. What is your percent error? What is 5.256X10-6 in standard format What is 118000 in scientific notation

Significant Figures in Measurements 3.1 Significant Figures in Measurements All measurement contains some degree of uncertainty. The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Measurements must always be reported to the correct number of significant figures Using pages 66-72 – fill in your notes regarding the rules of significant figures

Counting Significant Figures Number of Significant Figures 38.15 cm 4 5.6 ft 2 65.6 lb ___ 122.55 m ___ Complete: All non-zero digits in a measured number are (significant or not significant). Timberlake lecture plus

Timberlake lecture plus Leading Zeros Number of Significant Figures 0.008 mm 1 0.0156 oz 3 0.0042 lb ____ 0.000262 mL ____ Complete: Leading zeros in decimal numbers are (significant or not significant). Timberlake lecture plus

Timberlake lecture plus Sandwiched Zeros Number of Significant Figures 50.8 mm 3 2001 min 4 0.702 lb ____ 0.00405 m ____ Complete: Zeros between nonzero numbers are (significant or not significant). Timberlake lecture plus

Timberlake lecture plus Trailing Zeros Number of Significant Figures 25,000 in. 2 200 yr 1 48,600 gal 3 25,005,000 g ____ Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders. Timberlake lecture plus

Timberlake lecture plus Learning Check A. Which answers contain 3 significant figures? 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105 Timberlake lecture plus

Significant Figures in Calculations A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing Timberlake lecture plus

Timberlake lecture plus Adding & Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 answer 26.5 one decimal place Timberlake lecture plus

Timberlake lecture plus Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7 Timberlake lecture plus

Timberlake lecture plus Solution A. 235.05 + 19.6 + 2.1 = 2) 256.8 B. 58.925 - 18.2 = 3) 40.7 Timberlake lecture plus

Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Timberlake lecture plus

Multiplication + Division Answer should have the same number of significant figures as the measurement with the least. You may need to round your answer in order to achieve this

Timberlake lecture plus Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041 Timberlake lecture plus

Timberlake lecture plus Solution A. 2.19 X 4.2 = 2) 9.2 B. 4.311 ÷ 0.07 = 3) 60 C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060 Continuous calculator operation = 2.54 x 0.0028  0.0105  0.060 Timberlake lecture plus

Significant Figures in Calculations 3.1 Significant Figures in Calculations Rounding To round a number, you must first decide how many significant figures your answer should have. Your answer should be rounded to the number with the least amount of significant figures

How many significant figures are in the number QUIZ How many significant figures are in the number 603.040 b. 0.0828 c. 690,000 2. Perform the following operations and report to the correct number of sig. figs 4.15 cm X 1.8 cm 36.47 + 2.721 + 15.1 5.6 x 107 x 3.60 x 10-3

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