1 / 42

Significant Figures

Significant Figures. Part I: An Introduction. Objectives. When you complete this presentation, you will be able to distinguish between accuracy and precision determine the number of significant figures there are in a measured value. Introduction. Chemistry is a quantitative science.

beck-huff
Download Presentation

Significant Figures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Significant Figures Part I: An Introduction

  2. Objectives • When you complete this presentation, you will be able to • distinguish between accuracy and precision • determine the number of significant figures there are in a measured value

  3. Introduction • Chemistry is a quantitativescience. • We make measurements. • mass = 47.28 g • length = 14.34 cm • width = 1.02 cm • height = 3.23 cm

  4. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • volume = length × width × height

  5. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • volume = 14.34 cm × 1.02 cm × 3.23 cm

  6. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • volume = 47.244564 cm3

  7. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • volume = 47.244564 cm3 • density = mass ÷ volume

  8. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • volume = 47.244564 cm3 • density = 47.28 g ÷ 47.244564 cm3

  9. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • volume = 47.244564 cm3 • density = 1.000750055 g/cm3

  10. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • density = 1.000750055 g/cm3

  11. Introduction • Chemistry is a quantitativescience. • We make measurements. • We get lots of numbers. • We use those numbers to calculatethings. • density = 1.000750055 g/cm3 • What do these numbers mean? • Do we really know the density to the nearest 0.000000001 g/cm3 (= 1/1,000,000,000 g/cm3)?

  12. Accuracy and Precision • Accuracy and precision are often used to mean the same thing. • We expect that an accuratemeasurement is a precise measurement. • Likewise, we expect that a precisemeasurement is an accurate measurement. • They are related, but they are not the same thing.

  13. Accuracy and Precision • The accuracy of a series of measurements is how close those measurements are to the “real” value. • The “real” value of a measurement is usually the value acceptedby scientists. • It is usually based on a large number of measurements made by a large number of researchers over a long period of time.

  14. Accuracy and Precision • The accuracy of a series of measurements is how close those measurements are to the “real” value. • An example of accuracy is how close you come to the bullseye when shooting at a target. • Accurate shots come close to the bullseye. • Less accurate shots miss the bullseye.

  15. Accuracy and Precision • The precision of a series of measurements is how close the measurements are to each other. • Precise shots come close to each other. • Non-precise shots are not close to each other. • Which group has a greater accuracy? • The less precise group has a greater accuracy.

  16. Accuracy and Precision • When we are making a new measurement, we want to be as precise as possible. • We also want to be accurate, but usually our measurement devise is already accurate. • In most cases, inaccuracyin chemistry labs is due to misreadingthe instrument.

  17. Accuracy and Precision • When we are making a new measurement, we want to be as precise as possible. • Normally, we increase precision by making manymeasurements. • Then, we averagethe measurements.

  18. Accuracy and Precision • Example 1: • Ahab determines the density of a metal several times. • His measurements are: 7.65 g/cm3, 7.62 g/cm3, 7.66 g/cm3, and 7.63 g/cm3. • He reports his average density as 7.64 g/cm3.

  19. Accuracy and Precision • Example 1: • Brunhilda determines the density of a metal several times. • Her measurements are: 7.82 g/cm3, 8.02 g/cm3, 7.78 g/cm3, and 7.74 g/cm3. • She reports her average density as 7.84 g/cm3.

  20. Accuracy and Precision • Example 1: • Who is the most accurate? • Accuracy is related to how close you are to the accepted value. The accepted value is 7.84 g/cm3.

  21. Accuracy and Precision • Example 1: • Who is the most accurate? • Ahab’s data gives a value 0.20 g/cm3 from the accepted value. The accepted value is 7.84 g/cm3.

  22. Accuracy and Precision • Example 1: • Who is the most accurate? • Brunhilda’s data gives a value the same as the accepted value. The accepted value is 7.84 g/cm3.

  23. Accuracy and Precision • Example 1: • Who is the most accurate? • Therefore, Brunhilda is the most accurate. The accepted value is 7.84 g/cm3.

  24. Accuracy and Precision • Example 1: • Who is the most precise? • Ahab’s data varies from 7.62 to 7.66 g/cm3 - a spread of 0.04 g/cm3. The accepted value is 7.84 g/cm3.

  25. Accuracy and Precision • Example 1: • Who is the most precise? • Brunhilda’s data varies from 7.74 to 8.02 g/cm3 - a spread of 0.28 g/cm3. The accepted value is 7.84 g/cm3.

  26. Accuracy and Precision • Example 1: • Who is the most precise? • Ahab’s data was the most precise. The accepted value is 7.84 g/cm3.

  27. Significant Figures • But, what does this have to do with significant figures? • EVERYTHING!

  28. Significant Figures • The measurements we use in our calculations have a built-in precision. • When we find that the mass of an object is 47.28 g, we are saying that we know the mass of the object to a precision of 0.01 g (1/100 g). • So, we know the mass to be • (4×10) g + (7×1) g + (2×0.1) g + (8×0.01) g • We know the mass to 4 significant figures. 1 2 3 4

  29. Significant Figures • The measurements we use in our calculations have a built-in precision. • When we find that the mass of an object is 47.28 g, we are saying that we know the mass of the object to a precision of 0.01 g (1/100 g). • In the same way, we measure the length (14.34 cm), width (1.02 cm), and height (3.23 cm) to a precision of 0.01 cm. • We know the lengthto 4 significant figures.

  30. Significant Figures • The measurements we use in our calculations have a built-in precision. • When we find that the mass of an object is 47.28 g, we are saying that we know the mass of the object to a precision of 0.01 g (1/100 g). • In the same way, we measure the length (14.34 cm), width (1.02 cm), and height (3.23 cm) to a precision of 0.01 cm. • We know the widthto 3 significant figures.

  31. Significant Figures • The measurements we use in our calculations have a built-in precision. • When we find that the mass of an object is 47.28 g, we are saying that we know the mass of the object to a precision of 0.01 g (1/100 g). • In the same way, we measure the length (14.34 cm), width (1.02 cm), and height (3.23 cm) to a precision of 0.01 cm. • We know the heightto 3 significant figures.

  32. Significant Figures • It should be simple to tell how many significant figures there are in a measurement. • For example: if we measure the length of the room to be 14 meters, we have 2 significant figures. • But 14 m = 1400 cm • 1400 cm has 4 digits • It still has only 2 significant figures.

  33. Significant Figures • It should be simple to tell how many significant figures there are in a measurement. • For example: if we measure the length of the room to be 14 meters, we have 2 significant figures. • And, 14 m = 0.014 km • 0.014 has 4 digits • It still has only 2 significant figures.

  34. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 450,000 = 4.5 × 105 ➠ 2 significant figures

  35. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 0.03552 = 3.552 × 10−2 ➠ 4 significant figures

  36. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 14 = 1.4 × 101 ➠ 2 significant figures

  37. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 1,400 = 1.4 × 103➠ 2 significant figures

  38. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 0.014 = 1.4 × 10-2➠ 2 significant figures

  39. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 13.0 = 1.30 × 101➠ 3 significantfigures

  40. Significant Figures • We have rules for determining the number of significant figures in a measurement. • There is an easy way to determine the number of significant figures in a measurement. • We convert the number to scientific notation, and count the number of significant figures. 0.004200 = 4.200 × 10-3➠ 4 significantfigures

  41. Examples • How many significant figures are in each of the following numbers? • 4,210 m • 0.0002543 s • 5,100,000 kg • 0.745 mL • 4.324 cm • 0.00700 L 4.21×103 m ➠ 3 significant figures 2.543×10-4 s ➠ 4 significant figures 5.1×106 kg ➠ 2 significant figures 7.45×10-1 mL ➠ 3 significant figures 4.324×100 cm ➠ 4 significant figures 7.00×10-3 L ➠ 3 significant figures

  42. Summary • Accuracy relates to how close a value is to an accepted value. • Precision relates to how close individual measurements are to each other. • Significant figures are a measure of the precision of our measurements.

More Related