Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/1
© 2012 Pearson Education, Inc.
Accuracy: How close to the true value a given measurement is
Precision: How well a number of independent measurements agree with each other
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/2
© 2012 Pearson Education, Inc.
good accuracy
good precision
Mass of a Tennis Ball
(True Mass = 54.441 778 g)
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/3
© 2012 Pearson Education, Inc.
good accuracy
poor precision
Mass of a Tennis Ball
(True Mass = 54.441 778 g)
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/4
© 2012 Pearson Education, Inc.
poor accuracy
poor precision
Mass of a Tennis Ball
(True Mass = 54.441 778 g)
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/5
© 2012 Pearson Education, Inc.
Significant figures: The total number of digits recorded for a measurement
Generally the last digit in a reported measurement is uncertain (estimated).
Exact numbers and relationships (7 days in a week, 30 students in a class, etc.) effectively have an infinite number of significant figures.
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/6
© 2012 Pearson Education, Inc.
length = 1.74 cm
0
1
2
4
3
cm
1.7 cm < length < 1.8 cm
estimated value
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/7
© 2012 Pearson Education, Inc.
4.803 cm 4 SF
Rules for counting significant figures (left-to-right):
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/8
© 2012 Pearson Education, Inc.
0.006 61 g 3 SF (or 6.61 x 10-3 g)
Rules for counting significant figures (left-to-right):
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/9
© 2012 Pearson Education, Inc.
55.220 K 5 SF
Rules for counting significant figures (left-to-right):
Accuracy, Precision, and Significant Figures in Measurement
Chapter 1/10
© 2012 Pearson Education, Inc.
34,200 m ? SF
Rules for counting significant figures (left-to-right):
use scientific notation
Examples
Chapter 1/11
© 2012 Pearson Education, Inc.
Worked Example 1.4 Significant Figures
How many significant figures does each of the following measurements have?
(a) 0.036 653 m (b) 7.2100 × 10−3 g (c) 72,100 km (d) $25.03
Solution
(a) 5 (by rule 2) (b) 5 (by rule 3)
(c) 3, 4, or 5 (by rule 4) (d) $25.03 is an exact number
Rounding Numbers
Chapter 1/13
© 2012 Pearson Education, Inc.
11.70 gal
278 mi
= 23.8 mi/gal
4 SF
3 SF
3 SF
= 23.760 684 mi/gal
Math rules for keeping track of significant figures:
Rounding Numbers
Chapter 1/14
© 2012 Pearson Education, Inc.
3.19
+ 0.01 315
3.18
2 decimal places
5 decimal places
3.19 315
2 decimal places
Math rules for keeping track of significant figures:
Rounding Numbers
Chapter 1/15
© 2012 Pearson Education, Inc.
5.664 525 = 5.66
Rules for rounding off numbers:
Rounding Numbers
Chapter 1/16
© 2012 Pearson Education, Inc.
5.664 525 = 5.7
Rules for rounding off numbers:
Rounding Numbers
Chapter 1/17
© 2012 Pearson Education, Inc.
5.665 2 = 5.665
Rules for rounding off numbers:
Rounding Numbers
Chapter 1/18
© 2012 Pearson Education, Inc.
Rules for rounding off numbers:
5.664 56 = 5.664 6
Examples
Chapter 1/19
© 2012 Pearson Education, Inc.
Worked Example 1.5 A Calculation Using Significant Figures
Solution
First, set up an equation dividing the number of miles flown by the number of hours:
Next, decide how many significant figures should be in your answer. Because the problem involves a division, and because one of the quantities you started with (9.25 h) has only three significant figures, the answer must also have three significant figures. Finally, round off your answer. The first digit to be dropped (2) is less than 5, so the answer 427.243 24 must be rounded off to 427 mi/h.
It takes 9.25 hours to fly from London, England, to Chicago, Illinois, a distance of 3952 miles. What is the average speed of the airplane in miles per hour?
Worked Example 1.6 Unit Conversion Using Significant Figures
Strategy
The known information is the speed in mi/h; the unknown is the speed in km/h. Find the appropriate conversion factor inside the back cover of this book, and use the dimensional-analysis method to set up an equation so the “mi” units cancel.
Solution
A very fast car!
The Koenigsegg CCXR is the fastest sports car in the world, with a top speed of 265 miles per hour. What is this speed in kilometers per hour?
Worked Example 1.7 Unit Conversion Using Significant Figures
Strategy
We are given a gasoline mileage in L/km (or km/L), and we need to find the mileage in mi/gal. Thus, two conversions are necessary, one from kilometers to miles and one from liters to gallons. It’s best to do multiple conversions one step at a time until you get used to them. First, convert the distance from kilometers to miles and the amount of fuel from liters to gallons, and then divide the distance by the amount of fuel to find the mileage.
A large sport utility vehicle moving at a speed of 125 km/h might use gasoline at a rate of 16 L per 100 km. What does this correspond to in mi/gal?