SECTION 2.2MEASUREMENT UNCERTAINTIES

2.2 MEASUREMENT UNCERTAINTY

Problem of the Day1. 6.2 x 10-4 m + 5.7 x 10-3 m

2. 8.7x 108 km – 3.4 x 107 m

3. (9.21 x 10-5 cm)(1.83 x 108 cm)

4. (2.63 x 10-6 m) / (4.08 x 106 s)

2.2 MEASUREMENT UNCERTAINTY

Objectives Distinguish between accuracy and

precision. Indicate the precision of measured

quantities with significant digits. Perform arithmetic operations with

significant digits.

2.2 MEASUREMENT UNCERTAINTY

We must be certain that our experimental results can be reproduced again and again before they will

beaccepted as fact.

2.2 MEASUREMENT UNCERTAINTY

Comparing Results, p. 24 We are looking fro overlap between

experimental groups. Overlap indicates a common outcome.

2.2 MEASUREMENT UNCERTAINTY

Precision vs. Accuracy Precision – degree of exactness of a

measurement. Precision of a measurement depends

entirely on the device used to take it. Devices with finer divisions will give

more precise results.

2.2 MEASUREMENT UNCERTAINTY

Precision vs. Accuracy Meterstick – smallest division: 1mm –

precision: within 0.5mm Micrometer – smallest division: 0.01mm

– precision: within 0.005mm The micrometer is a more precise

instrument of measurement.

2.2 MEASUREMENT UNCERTAINTY

Precision vs. Accuracy Accuracy is about the “correctness” of a

measurement. Accuracy: How well does the measurement

compare with an accepted standard? Precision and Accuracy are used

interchangeable (and incorrectly) in common usage. We must be careful with these words here.

2.2 MEASUREMENT UNCERTAINTY

Precision vs. Accuracy Accuracy can be ensured by checking

our instruments. A common method is the two-point

calibration. Does the instrument read 0 when it is

should? Does it give the correct reading when

measuring an accepted standard?

2.2 MEASUREMENT UNCERTAINTY

Precision vs. Accuracy To ensure accurate and precise

measurements, the instruments must be used correctly.

Measurements should be taken while viewing the object and scale straight on.

If the reading is taken form the side, the reading can be off a little (because of something called parallax)

2.2 MEASUREMENT UNCERTAINTY

Significant Digits The valid digits in a measurement are

called significant digits. When you take a measurement, digits

up to and including the estimated digit are significant.

The last digit in any measurement is referred to as the uncertain digit.

2.2 MEASUREMENT UNCERTAINTY

Significant Digits If the object lands exactly on a division

of the device, you should report the final digit as 0 so the reader knows that the measurement is exact.

Rules for Significant Digits Nonzero digits are always significant. All final zeros after the decimal point are

significant.

2.2 MEASUREMENT UNCERTAINTY

Significant Digits Rules for Significant Digits (cont.)

Zeros between two significant digits are always significant.

Zeros used solely as placeholders are not significant.

All of the following have three significant digits:

245 m 18.0 g 308 km 0.00623 gPractice 15-16, p. 27

2.2 MEASUREMENT UNCERTAINTY

Arithmetic with Significant Digits When adding or subtracting measurements,

the answer can be no more precise than the least precise measurement in the calculation.

Ex. 24.686m + 2.343m + 3.21m = 30.239m, but the correct answer is

30.24We must round the answer to two decimal places because 3.21 has only 2 places

2.2 MEASUREMENT UNCERTAINTY

Arithmetic with Significant Digits When multiplying or dividing measurements,

the answer can have no more significant digits than the measurement with the smallest number.

Ex. 3.22cm x 2.1cm = 6.762cm2, but the correct answer is

6.8cm2

We must round the answer to two sig. dig. places because 2.1 has only 2 sig. dig.

Practice 17-20, p. 28

2.2 MEASUREMENT UNCERTAINTY

Arithmetic with Significant Digits Important Note 1: These rules above

apply only to measurements. There are no significant digits issue involved when counting.

Important Note 2: Be careful of calculators. They do not concern themselves with significant digits. You need to.

2.1 THE MEASURES OF SCIENCE

Assignment: p. 38-40, #’s 34-43 Key Terms for section 2.2 from p. 37

into your notebook.