How big is the beetle? Measure between the head and the tail! Between 1.5 and 1.6 in Measured length: 1.54 in The 1 and 5 are known with certainty The last digit (4) is estimated between the two nearest fine division marks. Copyright © 1997-2005 by Fred Senese

Chapter One: Measurement 1.4 Working with Measurements

1.4 Working with Measurements Accuracy is how close a measurement is to the accepted, true value. Precision describes how close together repeated measurements or events are to one another.

1.4 Working with Measurements In the real world it is impossible for everyone to arrive at the exact same true measurement as everyone else. Find the length of the object in centimeters. How many digits does your answer have?

1.4 Working with Measurements Digits that are always significant: Non-zero digits. Zeroes between two significant digits. All final zeroes to the right of a decimal point. Digits that are never significant: Leading zeroes to the right of a decimal point. (0.002 cm has only one significant digit.) Final zeroes in a number that does not have a decimal point.

Significant digits in mathematical operations For multiplication or division, the number of significant digits in the result is the same as the number in the least precise measurement used in the calculation. 1.342 × 5.5 = 7.381  7.4

Significant digits in Mathematical Operations For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.

What is area of 8.5 in. x 11.0 in. paper? Looking for: Given: Solving Problems What is area of 8.5 in. x 11.0 in. paper? Looking for: …area of the paper Given: … width = 8.5 in; length = 11.0 in Relationship: Area = W x L Solution: 8.5 in x 11.0 in = 93.5 in2 # Sig. fig = 94 in2

1.4 Working with Measurements Using the bow and arrow analogy explain how it is possible to be precise but inaccurate with a stopwatch, ruler or other tool.

1.4 Resolution Resolution refers to the smallest interval that can be measured. You can think of resolution as the “sharpness” of a measurement.

1.4 Significant differences In everyday conversation, “same” means two numbers that are the same exactly, like 2.56 and 2.56. When comparing scientific results “same” means “not significantly different”. Significant differences are differences that are MUCH larger than the estimated error in the results.

1.4 Error and significance How can you tell if two results are the same when both contain error (uncertainty)? When we estimate error in a data set, we will assume the average is the exact value. If the difference in the averages is at least three times larger than the average error, we say the difference is “significant”.

1.4 Error How you can you tell if two results are the same when both contain error. Calculate error Average error Compare average error

Is there a significant difference in data? Looking for: Given: Solving Problems Is there a significant difference in data? Looking for: Significant difference between two data sets Given: Table of data Relationships: Estimate error, Average error, 3X average error Solution: There is not a significance difference between 0.3352 and 0.3349 because: 0.3352-0.3349= 0.0003 and 3x0.0002=0.0006 0.0003< 0.0006