1. Chemistry Chapter 2D Uncertainty in Measurement

2. Uncertainty  Represents how well a measurement was made  Science is ‘peer reviewed’  We don’t just take one person’s word for it  To evaluate properly, we must know how well measurements have been made  Two ways of looking at measurements  Accuracy  How closely does measured value agree with standard  Precision  How carefully was the measurement made  Depends in part on measuring instrument

3. Error  Percent error is a way of representing difference between measured values and standard values  Percent error = standard – measured x 100 standard

4. Sample Problem 2-3 A student measures the mass and volume of a substance and calculates its density as 1.40 g/ml. The correct, or accepted value of the density is 1.36 g/ml. What is the percent error of the measurement?

5. Significant Digits Method of representing precision of measurements Represented both by method of reporting measurement and in calculations with that measurement Generally: read smallest possible division of instrument and estimate fraction

6. Example  Here is the readout of a Vernier micrometer  The measurement is 7.380 mm

7. Rules Rules for significant digits: ▫Nonzero numbers ARE significant ▫Zeros AFTER (to the right) the decimal ARE significant ▫Zeros BETWEEN to nonzero numbers ARE significant ▫Zeros BEFORE the decimal (and not between nonzero numbers) are NOT significant

8. Sample Problem 2-4 How many significant figures are in each of these measurements? 28.6 g 3440. cm 910 cm 0.046 04 L 0.006 700 0 kg

9. Rules for Operations Addition and subtraction: ▫The PLACE VALUE (what column the significant digits are in) determines the last reported value ▫Example p 17

10. Rules for operations Multiplication and division: ▫The answer is reported using the LEAST number of significant digits of the starting numbers ▫Sample Problem 2-5 p 49