Presentation on theme: "Using and Expressing Measurements"— Presentation transcript:
1 Using and Expressing Measurements 3.1Using and Expressing MeasurementsUsing and Expressing MeasurementsHow do measurements relate to science?
2 Using and Expressing Measurements 3.1Using and Expressing MeasurementsA 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.
4 Scientific Notation210, 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?
5 210, 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
6 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 right4,580, 000
7 express the number 0. 000000345 in scientific notation express the number in scientific notation. Decimal moved between first 2 non-zero digits and will be moved 7 times 3.45 x The exponent is negative because the original number is a very small number
8 Express the following in scientific notation or standard notation x x 106
9 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorAccuracy, Precision, and ErrorWhat is the difference between accuracy and precision?
10 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorAccuracy and PrecisionAccuracy 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.
11 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorTo 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.
12 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorThe 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.
13 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorDetermining ErrorThe 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.
14 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorThe percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.Experimental – knownExpressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.
15 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorPercent Error (Error) 3.00-measurement X
16 Accuracy, Precision, and Error 3.1Accuracy, Precision, and ErrorJust 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?
19 % ERRORThe 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 formatWhat is in scientific notation
20 Significant Figures in Measurements 3.1Significant Figures in MeasurementsAll 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 figuresUsing pages – fill in your notes regarding the rules of significant figures
21 Counting Significant Figures Number of Significant Figures38.15 cm 45.6 ft 265.6 lb ___m ___Complete: All non-zero digits in a measured number are (significant or not significant).Timberlake lecture plus
22 Timberlake lecture plus Leading ZerosNumber of Significant Figures0.008 mm 1oz 3lb ____mL ____Complete: Leading zeros in decimal numbers are (significant or not significant).Timberlake lecture plus
23 Timberlake lecture plus Sandwiched ZerosNumber of Significant Figures50.8 mm 32001 min 40.702 lb ____m ____Complete: Zeros between nonzero numbers are (significant or not significant).Timberlake lecture plus
24 Timberlake lecture plus Trailing ZerosNumber of Significant Figures 25,000 in200 yr 148,600 gal 325,005,000 g ____Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.Timberlake lecture plus
25 Timberlake lecture plus Learning CheckA. Which answers contain 3 significant figures?) ) 4760B. All the zeros are significant in1) ) ) x 103C. 534,675 rounded to 3 significant figures is1) ) 535, ) 5.35 x 105Timberlake lecture plus
26 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 from1) adding or subtracting2) multiplying or dividingTimberlake lecture plus
27 Timberlake lecture plus Adding & SubtractingThe answer has the same number of decimal places as the measurement with the fewest decimal places.one decimal placetwo decimal places26.54answer one decimal placeTimberlake lecture plus
28 Timberlake lecture plus Learning CheckIn each calculation, round the answer to the correct number of significant figures.A =1) ) ) 257B =1) ) ) 40.7Timberlake lecture plus
29 Timberlake lecture plus SolutionA =2) 256.8B =3) 40.7Timberlake lecture plus
30 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
31 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
32 Timberlake lecture plus Learning CheckA X 4.2 =1) ) )B ÷ =1) ) ) 60C X =X 0.0601) ) )Timberlake lecture plus
33 Timberlake lecture plus SolutionA X = 2) 9.2B ÷ = 3) 60C X = 2) X 0.060Continuous calculator operation =x Timberlake lecture plus
34 Significant Figures in Calculations 3.1Significant Figures in CalculationsRoundingTo 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
35 How many significant figures are in the number QUIZHow many significant figures are in the numberb c. 690,0002. Perform the following operations and report to the correct number of sig. figs4.15 cm X 1.8 cm5.6 x 107 x 3.60 x 10-3