Problem of the Day x m x m x 10 8 km – 3.4 x 10 7 m 3. (9.21 x cm)(1.83 x 10 8 cm) 4. (2.63 x m) / (4.08 x 10 6 s)

Objectives  Distinguish between accuracy and precision.  Indicate the precision of measured quantities with significant digits.  Perform arithmetic operations with significant digits.

We must be certain that our experimental results can be reproduced again and again before they will be accepted as fact.

 Comparing Results, p. 24  We are looking fro overlap between experimental groups.  Overlap indicates a common outcome.

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.

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.

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.

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?

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)

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.

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.

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 g Practice 15-16, p. 27

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 m m m = m, but the correct answer is We must round the answer to two decimal places because 3.21 has only 2 places

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 = 6.762cm 2, but the correct answer is 6.8cm 2 We must round the answer to two sig. dig. places because 2.1 has only 2 sig. dig. Practice 17-20, p. 28

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.

 Assignment: p , #’s  Key Terms for section 2.2 from p. 37 into your notebook.