Measurements and Sig Figs

The Quality of Experimental Results Accuracy: how close a measured value is to the actual (true) value. Precision: how close the measured values are to each other. Examples of Precision and Accuracy: Precise but not accurate Accurate but not precise Accurate and precise

Reliability: the consistency or repeatability of your measurement. Validity: how close your measurements are to the accepted value. For example: You are given a 100g weight to mass on an electronic balance. If your scale were to repeatedly measure g we could say that it is very precise (results are reliable), but not very accurate (results are not valid).

Increasing reliability and validity You could get state of the art lab equipment and a team of science geniuses to do your labs for you... OR, you can properly control variables, eliminate bias, and use measuring instruments appropriate to the task at hand

Measurements and uncertainty You can only be as precise as your measuring instrument allows you to be. Uncertainty for a measurement is equivalent to +/- 0.5 of the smallest measurement Ex. This object measures 4.40 cm +/- 0.5 mm (last digit is uncertain) You might say 4.39 or 4.41, but you cannot add any more decimal places

Other examples: How much fluid is in this graduated cylinder? (73.0 ml +/- 0.5 ml) What is the temperature? (38.45 o C +/- 0.5 o C )

What are Significant Figures? (as opposed to significant figurines...)

Sig figs help us understand how precise measurements are Using sig figs increases accuracy and precision Sig figs cut down on error caused by improper rounding HOORAY FOR SIG FIGS!!! SIG FIGS RULE

Which digits are significant?significant Rule #1: All non-zero digits are significant. o24 has two sig figs, 24.1 has 3 sig figs Rule #2: All zeros bounded by non-zero integers are significant o2004 has four sig figs, also has 4 sig figs Rule #3: Zeros placed before other digits (leading zeros) are not significant o0.024 has 2 sig figs Rule #4: Zeros at the end of a number are significant ONLY if they come after a decimal point o2.40 has three sig figs, 240 only has 2 sig figs

Practice: How many sig figs? o409.25o o83o o98.207o 5.5 x 10 2 o0.001o o4.3 x 10 2 o o o o4200o o0.9106o o0.200o

Rules for Multiplication and Division The number of sig figs in the answer should be the same as in the number with the least sig figs being multiplied or divided. oEx. 7.3 x 1264 = oThe answer must only contain 2 sig figs, so we use scientific notation oThe answer becomes 9.2 x 10 3 oThis answer contains 2 sig figs

Ex x x 1376 = Ex x x 0.04 = Ex x x = Ex x 14 x =