Chemistry Chapter 2D Uncertainty in Measurement

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

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

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?

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

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

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

Sample Problem 2-4 How many significant figures are in each of these measurements? 28.6 g cm 910 cm L kg

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

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