Lesson 7 Reliability, Significant Figures and Percent Error

I.Reliability of Measurements A.Measurements must be made with care 1.No measurement is completely exact a.Human error b.Instrument error c.Method error 2. These errors should be accounted for in any report on an experiment.

B.Accuracy differs from precision 1.Accuracy is the extent to which a measurement approaches the exact value and is free from error 2.Precision is how exactly or sharply stated a measurement is. 3.Precision can also indicate how close together a group of measurements are. 4.You can have measurements which are both accurate and precise, not accurate or precise, or precise but not accurate (measurements close together, but not close to the correct value)

Significant figures: a definition Significant figures, sometimes called significant digits, or even sig. figs. for short, are digits in a measurement which have actually been measured by comparison with scale, plus one estimated digit. This is a direct indication of how accurate your measurements or calculations are.

Rules for determining whether a digit is significant or not. Rule 1: All non-zero numbers are significant. Ex. 1,2,3,4,5,6,7,8,9 Rule 2: Zeroes appearing between significant figures are also significant. Ex. 202, 40009, Rule 3: Zeros at the very end of a decimal are significant. Ex. 4.80, Rule 4: Zeros that are place holders only are NOT significant. They are not in between sig figs or at the end of the decimal. Ex

Examples: , , , ,

In the case of unclarity, you may indicate the last significant figure with a bar above it. A decimal may also be used to indicate significance of zeros:

Rules for Calculations in terms of Significant Figures: In scientific calculations, your answers are only allowed to be as accurate as your least accurate measurement in the problem. This is of utmost importance when doing research. Answers in which significant figures rules are not followed are considered COMPLETELY INVALID AND MEANINGLESS!!! Learn these rules now and live by them! You will be held to them in all calculations in my class, in physics next year and any math based science class you ever take from now on.

Rules for Multiplication or Division: Look at all the numbers in the math problem. Identify how many significant figures are in each of the factors. Your answer to the problem may only have as many significant figures as the smallest number in the original math problem.

Example: x 8.30 The first factor has 5 sig figs and the second factor has 3 sig figs. When you type this into your calculator, it gives an answer of : This number has 6 significant figures. Our final answer is only allowed to have 3. Round your answer using normal rounding rules. Final answer is :102

Rules for Calculations with Addition or Subtraction: In an addition or subtraction problem, we are not concerned with the number of significant figures in each term, but how many decimal places are present in each. The final answer may only have as many decimal places as the fewest present in the original problem.

Example: =

III.Percent Error A.Percent Error shows the accuracy of experimental data obtained in the laboratory. B.To Calculate Percent Error 1.First take the absolute value of the experimental number (number obtained in your experiment) and subtract the accepted value (theoretical value) This difference is called the Error 2.Percent error is then the (Error divided by the accepted value) times 100 to give you a percentage. (Error) X 100 (Accepted Value)

Example: Your experiment predicts the mass of an oxygen atom to be and you are told that the known value is actually what is the percent error of your calculation? %

Example 2: Your calculation predicts the mass of a product to be 5.00 g and you physically, in an experiment, massed the product to be 4.5 g. What is the percent error of your calculation? 10 %

Accuracy vs. Precision Questions: –Compare and Contrast Accuracy and Precision. –Tell whether each of the following situations describes accuracy, precision, both, or neither: a. 15 cm, 2.16 cm, 2.12 cm, 2.21 cm (Actual length 2.19 cm) b L, 92.8 L, 56.0 L (Actual volume 79.1 L) c g, g, g (Actual mass g) d mL, mL, mL, mL (Actual volume mL)

Level 1 1.How many significant figures are there in each of the following measurements? A.23 cm B g C s D mL E kg F.32.8 m G.107 mm H km I cm J m 2.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for addition and subtraction. A.3.42 cm cm B g g C.17.8 cm cm D kg kg E s s F g g G cm cm H m m I g g J.133 L L 3.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for multiplication and division. A.1.2 cm x 1.3 cm B.2.1 m x 1.8 m C.1.45 m x 2.2 m D.2.5 mm x 1.33 mm E km x 1.2 km F m2 / m G.16.5 km2 / 1.8 km H m2 / 2.63 m I.9.9 mm2 / mm J cm2 / cm

Level 2 1.How many significant figures are there in each of the following measurements? A.722 g B mL C hL D L E cm F mm G km H g I kg J m 2.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for addition and subtraction. A.72 cm + 48 cm B m m C.888 g g D mm mm E mg mg F cm cm G.4.2 kg kg H.883 m m I cm cm J g g 3.Express the answer to each of the following calculations with the correct number of significant figures. Remember the rules for multiplication and division. A.8.3 cm x 87 cm B.76.0 m x 45 m C mm x mm D km x 13.1 km E.711 m x 8.3 m F mm2 / 83.3 mm G.7.34 m2 / 0.25 m H mm2 / 76 mm I km2 / km J.67.2 km2 / km

Level 3 1. How many significant figures are there in each of the following measurements? A.307 g B cm C g D mm E.4500 km F.350,000 cm G s H.3.50 x 103 cm I x 10-4 m J x 103 g 2. Express the answer to each of the following calculations with the correct number of significant figures. A.80 cm cm B m m C cm cm D.1.30 x 10-2 cm x 10-4 cm E.8.99 x 103 m x 104 m F.750. cm – cm G.10,000 m – 940 m H cm – cm I x 10-1 g – 1.20 x 10-2 g J.4.5 x 105 km – 3.00 x 103 km 3. Express the answer to each of the following calculations with the correct number of significant figures. A.3.0 cm x cm B cm x 5.0 cm C.400 m x 87,488 m D.2.3 x 10-6 m x 1.40 x 10-2 m E.8.70 x 10-2 mm x 40. x 10-1 mm F mm2 / 0.90 mm G.120 km2 / 8.56 km H mm3 / 1.50 mm I.4.80 x 105 m2 / 8.5 x 103 m J x 10-1 m3 / x 102