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Words to Know Qualitative measurements – results are in a descriptive, nonnumeric form (Forehead feels hot) Quantitative – results are in a definite form, usually as numbers or units (Temperature is 102 0 F)

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Objectives Distinguish among the accuracy, precision, and error of a measurement Identify the number of significant figures in a measurement and in the result of a calculation

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Words to Know Accuracy – a measure of how close a measurement comes to the actual or true value of whatever is measured (Closeness of a dart to the bull’s-eye) Precision – a measure of how close a series of measurements are to one another; depends on more than one measurement (The closeness of several darts to one another- reproducibility)

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Accepted value – correct value based on reliable references (Example: Boiling point of pure water is 100 0 C at standard atmospheric pressure) Experimental value – value measured in the lab Error = experimental value minus accepted value Error can be positive or negative number

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Practice A thermometer measures the boiling point of pure water at standard atmospheric pressure. It reads 99.1 0 C. What is the accepted value? What is the experimental value? What is the error? Ans. – Acc (100 0 C) Exp (99.1 0 C) Error is 99.1 0 C – 100 0 C, or -0.9 0 C

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Percent Error (Relative Error) Percent error is the absolute value of the error divided by the accepted value, multiplied by 100% Using absolute value means that the percent error will always be a positive value Calculate the percent error for the boiling pure water

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Answer Percent error = (absolute value of the error ÷ accepted value) x 100%.9 0 C ÷ 100.0 0 C = 0.009 0.009 x 100% Move decimal point two places to the right Answer is 0.9%

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Significant Figures All the digits that are known, plus a last digit that is estimated Every non-zero digit is significant. Examples: There are three significant figures in 24.7 meters, 0.743 meters, and 714 meters. Zeros appearing between non-zero digits are significant. Examples: There are four significant digits in 7003 meters, 40.79 meters, and 1.503 meters.

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Leftmost zeros appearing in front of non-zero digits are not significant. They act as placeholders. Examples: 0.0071 meter, 0.42 meter, and 0.000099 meter each have only two significant figures. Write these numbers in scientific notation to get rid of placeholding zeros.

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Answers Decimal point moves to the right, so all exponents will be negative numbers 7.1 x 10 -3 meter 4.2 x 10 -1 meter 9.9 x 10 -5 meter

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Zeros at the end of a number and to the right of a decimal point are always significant. Examples: 43.00 meters, 1.010 meters, and 9.000 meters each have four significant figures

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In a number that has no decimal point, zeros at the rightmost end of the measurement are not significant if they serve as placeholders to show the magnitude of the number. Examples: 2500 meters 460,000 meters, and 16,000 meters each have 2 significant figures If such zeros were known measured values, however, then they would be significant and should be written in scientific notation.

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Examples: 300 meters and 7000 meters each have one significant figure If the zeros are known measured values, record them as 3.00 x 10 2 meters and 7.00 x 10 3 meters The measurement 27210 has four significant figures.

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Atlantic/Pacific Rule If a decimal point is present, count from this side starting with the first non- zero digit and keep counting until there are no remaining digits. If a decimal point is absent, count from this side starting with the first non- zero digit and keep counting until there are no remaining digits.

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Measurements with an Unlimited Number of Significant Digits 1. Counting Example: 23 people in the classroom (Not 22.9 or 23.1) 23.00000000………………………….. 2. Exactly defined quantities Example: 60 minutes = 1 hour 60.00000000…………………………..

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Identify the Number of Significant Figures 4.0 x 10 3 1.67 x 10 -8 5201 635.000 22 000 0.00530 200.0 400 218 4755.50

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Significant Figures in Calculations Calculation cannot be more exact than the measured values used to obtain it Example: Find the area of a floor measures 7.7 meters by 5.4 meters Each measurement has only two significant figures Calculator reads 41.58 square meters

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If the digit immediately to the right of the last significant digit is less than 5, it is dropped If it is 5 or greater, the value of the last significant digit is increased by 1 41.58 square meters becomes 42 square meters

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Practice Problems Round each measurement to two significant figures. Write your answers in scientific notation. A. 94.592 grams B. 2.4232 x 10 3 grams C. 0.007 438 grams D. 54 752 grams E. 6.0289 x 10 -3 grams F. 405.11 grams

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Answers A. 9.5 x 10 1 grams B. 2.4 x 10 3 grams C. 7.4 x 10 -3 grams D. 5.5 x 10 4 grams E. 6.0 x 10 -3 grams F. 4.1 x 10 2 grams

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Calculation Rules Multiplication and Division – round the answer to the same number of significant figures as the measurement with the least number of significant figures Addition and Subtraction – the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places

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