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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. - PowerPoint PPT Presentation
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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.– We make measurements.• mass = 47.28 g• length = 14.34 cm• width = 1.02 cm• height = 3.23 cm
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• volume = length × width × height
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• volume = 14.34 cm × 1.02 cm × 3.23 cm
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• volume = 47.244564 cm3
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• volume = 47.244564 cm3
• density = mass ÷ volume
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• volume = 47.244564 cm3
• density = 47.28 g ÷ 47.244564 cm3
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• volume = 47.244564 cm3
• density = 1.000750055 g/cm3
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• density = 1.000750055 g/cm3
Introduction
• Chemistry is a quantitative science.– We make measurements.– We get lots of numbers.– We use those numbers to calculate things.• 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)?
Accuracy and Precision
• Accuracy and precision are often used to mean the same thing.– We expect that an accurate measurement is a
precise measurement.– Likewise, we expect that a precise measurement is
an accurate measurement.• They are related, but they are not the same
thing.
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 accepted by scientists.– It is usually based on a large number of
measurements made by a large number of researchers over a long period of time.
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.
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.
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, inaccuracy in chemistry labs is due
to misreading the instrument.
Accuracy and Precision
• When we are making a new measurement, we want to be as precise as possible.
• Normally, we increase precision by making many measurements.
• Then, we average the measurements.
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.
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.
Accuracy and Precision
• Example 1:• Who is the
most accurate?• Accuracy is
related to how close you are to the accepted value.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
Accuracy and Precision
• Example 1:• Who is the
most accurate?• Ahab’s data
gives a value 0.20 g/cm3 from the accepted value.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
Accuracy and Precision
• Example 1:• Who is the
most accurate?• Brunhilda’s
data gives a value the same as the accepted value.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
Accuracy and Precision
• Example 1:• Who is the
most accurate?• Therefore,
Brunhilda is the most accurate.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
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.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
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.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
Accuracy and Precision
• Example 1:• Who is the
most precise?• Ahab’s data
was the most precise.
Measurement Ahab Brunhilda
1 7.65 g/cm3 7.82 g/cm3
2 7.62 g/cm3 8.02 g/cm3
3 7.66 g/cm3 7.78 g/cm3
4 7.63 g/cm3 7.74 g/cm3
Average 7.64 g/cm3 7.84 g/cm3
The accepted value is 7.84 g/cm3.
Significant Figures
• But, what does this have to do with significant figures?
• EVERYTHING!
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
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 length to 4 significant figures.
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 width to 3 significant figures.
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 height to 3 significant figures.
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.
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.
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➠
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➠
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➠
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➠
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➠
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 significant figures➠
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 significant figures➠
Examples
• How many significant figures are in each of the following numbers?
1. 4,210 m2. 0.0002543 s3. 5,100,000 kg4. 0.745 mL5. 4.324 cm6. 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
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.