 # MEASUREMENT 1.4.

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MEASUREMENT 1.4

Chapter One: Measurement
1.1 Measurements 1.2 Time and Distance 1.3 Converting Measurements 1.4 Working with Measurements

Section 1.4 Learning Goals
Determine the number of significant figures in measurements. Distinguish accuracy, precision, and resolution. Compare data sets to determine if they are significantly different.

Conversion Chains Investigation 1B Key Question:
How can you use unit canceling to solve conversion problems?

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.

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: Math answer: in2 Determine # of significant figures = 94 in2

Significant Digits Investigation 1C Key Question:
How do we make precise measurements?

Nanotechnology What if biological nanomachines could seek out a broken part of a cell and fix it? How can a nanomachine mimic nature’s ability to heal? These are the cutting-edge questions that nanomedicine scientists are trying to answer.