Measurement In Science: Certainty in Measurement: Accuracy, Precision and Significant Figures Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

Certainty in measurement When measuring quantitative properties of matter you must use a measuring instrument. Measuring instruments are generally graduated- made with marks to show levels of amounts Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All right reserved.

Certainty in measurement Some measuring instruments are more exact than others. This means that every instrument has a certain level of uncertainty- inexactness It is important to be clear about how exact and reliable a measurement is, so that you can decide whether it is trustworthy or not Chapter menu Resources Copyright © by Holt, Rinehart and Winston. All rights reserved.

ACCURACY vs. PRECISION Accuracy indicates how close a measurement is to the real amount. Precision indicates how close together or how repeatable the results are. A precise measuring instrument will give very nearly the same result each time it is used. ( Of course the repeated measurement, may or may not be accurate!)

QUESTION 1: HORSESHOES & HAND GRENADES Watch 3 balls drop and say good or bad for precision and accuracy PRECISION ? GOOD! (HIGH) REASON: All 3 of the results are close to each other Target ACCURACY? POOR! (LOW) REASON: All 3 results are WAY off the “actual” targeted value

HORSESHOES & HAND GRENADES QUESTION 2: Watch 3 balls drop and say good or bad for precision and accuracy PRECISION ? POOR! (LOW) REASON: All 3 results are nowhere close to one another ACCURACY? POOR! (LOW) REASON: All 3 results come nowhere near the “actual” targeted amount

HORSESHOES & HAND GRENADES QUESTION 3: Watch 3 balls drop and say good or bad for precision and accuracy PRECISION ? GREAT! (High) REASON: All 3 results are right next to each other ( little difference) ACCURACY? GREAT! (High) REASON: All 3 results are RIGHT ON the targeted “actual” amount

HORSESHOES & HAND GRENADES QUESTION 4: Watch 3 balls drop and say good or bad for precision and accuracy PRECISION ? PRETTY GOOD! (High) REASON: All 3 are FAIRLY CLOSE to each other (not much difference) ACCURACY? PRETTY GOOD! (High) REASON: All 3 are FAIRLY CLOSE to the targeted “actual” amount. (not much difference)

EXAMPLE :ACCURACY Accurate Innacurate 100g 100g 98.89g 100.00g Example: We'd expect a balance to read 100 grams if we placed a standard 100 g weight on the balance. If it does not, then the balance is inaccurate. (It does not come close to the “actual mass”)

EXAMPLE : PRECISION More Precise Less Precise Trial # Mass (g) 1 100.00 2 100.01 3 99.99 4 Average Range ± 0.01 Std. Dev. 0.05 Trial # Mass (g) 1 100.10 2 100.00 3 99.88 4 100.02 Average Range ± 0.11 Std. Dev. 0.09 Example: Notice that the 4 measurements on the right are not as close to each other as the 4 readings on the right. They have less Precision

Reporting Measurements Report what is known with certainty Add ONE digit of uncertainty (estimation) By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement. Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Measuring a Pin Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122

Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 4 1 2 3 4 5 4.5 cm PRACTICE MEASURING Estimate one digit of uncertainty. a) 4.5 cm b) * 4.55 cm c) 3.0 cm *4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor) By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement. In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation. How could the measurement be affected by the use of several different rulers to measure the red wire? (Different rulers could yield different readings depending on their precision.) Why is it important to use the same measuring instrument throughout an experiment? (Using the same instrument reduces the discrepancies due to manufacturing defects.) cm 1 2 3 4 5 4.54 cm cm 1 2 3 4 5 3.0 cm Timberlake, Chemistry 7th Edition, page 7

Implied Range of Uncertainty 5 6 4 3 Implied range of uncertainty in a measurement reported as 5 cm. When the plus-or-minus notation is not used to describe the uncertainty in a measurement, a scientist assumes that the measurement has an implied range, as illustrated above. The part of each scale between the arrows shows the range for each reported measurement. 5 6 4 3 Implied range of uncertainty in a measurement reported as 5.0 cm. 5 6 4 3 Implied range of uncertainty in a measurement reported as 5.00 cm. Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

20 ? 15 mL ? 1.50 x 101 mL 15.0 mL A student reads a graduated cylinder that is marked at 15.00 mL, as shown in the illustration. Is this correct? NO Express the correct reading using scientific notation. 15.0 mL or 1.50 x101 mL 10

How to Read a Thermometer (Celcius) 10 10 100 5 5 5 50 4.0 oC 8.3 oC 64 oC 3.5 oC

Record the Temperature (Celcius) 60oC 6oC 50oC 5oC 25oC 100oC 100oC 40oC 4oC 20oC 80oC 80oC 30oC 3oC 15oC 60oC 60oC 20oC 2oC 10oC 40oC 40oC 10oC 1oC 5oC 20oC 20oC 0oC 0oC 0oC 0oC 0oC A 30.0oC 48oC 60.oC B 3.00oC C 19.0oC D E

Accuracy vs. Precision ACCURATE = Correct PRECISE = Consistent Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = Correct PRECISE = Consistent Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Accuracy vs. Precision Systematic errors: reduce accuracy Scientists repeat experiments many times to increase their accuracy. Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy Random errors: reduce precision (instrument) (person)

Precision Accuracy check by check by using a repeating                                                                                                                                                        Precision Accuracy reproducibility check by repeating measurements poor precision results from poor technique correctness check by using a different method poor accuracy results from procedural or equipment flaws. http://antoine.frostburg.edu/chem/senese/101/measureme nt/slides/sld016.htm

Types of errors Systematic Random Instrument not ‘zeroed’ properly Reagents made at wrong concentration Random Temperature in room varies ‘wildly’ Person running test is not properly trained