Accuracy and Precision Measurements Significant Figures (Sig Figs)

Accuracy vs. Precision Accuracy - refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision - refers to the closeness of a set of measurements of the same quantity made in the same way.

Accurate or Precise?

Cubes from yesterday

Percent Error Calculated by subtracting the experimental value (the value you find) from the accepted value (“correct value”), dividing the difference by the accepted value, and then multiplying by 100. % error = Value (accepted) - Value (experimental) x 100 Value (accepted)

PRACTICE: Calculate the percent error in a length measurement of 4 PRACTICE: Calculate the percent error in a length measurement of 4.25 cm if the correct value is 4.08 cm % error = 4.08 cm - 4.25 cm x 100 4.08 cm % error = -4.2% The % error has a negative value because the accepted value is less than the experimental value. If positive, the accepted value is greater than the experimental value.

Error in Measurement Uncertainty exists in any measurement. Skill of the measurer and the measuring instruments themselves place limitations on accuracy.

Estimation In any measurement, you can estimate the value of the final questionable digit, and you might include a plus-or-minus value to express the range. EXAMPLE: How long is the beetle? 1.54 ±0.02 in.

Practice: Which digit is uncertain? Measurement ** Always read as many places as possible from the instrument and then estimate one additional place. The last number that you record is the one you are uncertain about Practice: Which digit is uncertain? 43.29 23 184.2 43.29 23 184.2

Example: An instrument reads to the nearest tenth Example: An instrument reads to the nearest tenth. You should estimate to the nearest _________________. hundredth Example: A scientist records a measurement as 23.4 mL. The instrument must have ______________ increments. 1 mL

How long is the yellow cylinder? 1.25 cm (but you could say any # for the 5 and still be correct! The 5 is the estimated digit since the instrument measures to the tenths place)

Estimate one spot past the line you can see If markings are given every 10 ml… Estimate to the 1’s place (ex: 15 ml) If markings are given every 1 ml… Estimate to the tenths place (ex: 15.0) If markings are given every 0.1 ml… Estimate to the hundreths place (ex: 15.00)

The unusual cases If markings are given for 0.2 ml… Still estimate to the 100th place (ex: 15.25) If markings are given every 25 or 50 ml… Don’t use as a measuring device!! If you DO use it to measure, measurements should be something like “90ml”, not “90.0 ml”

VOLUME OF A LIQUID: UNITS: mL What is this curved line called? Meniscus Do you measure the amount of liquid at the highest part of the meniscus or the lowest part? LOWEST (Bottom) How much water is in this graduated cylinder to the correct number of DECIMALS? 43.0

3 Stations Round 1 on worksheet Answers: 50 mL graduated cylinder should have 1 decimal place 10 mL graduated cylinder should have 2 decimal places Quadruple beam balance should have 3 decimal places

Significant Digits (Also Called Significant Figures – Abbreviated as sig. figs.) When measuring an object (like length, mass, volume, etc.) the significant figures consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. You’ll need to know the rules for working with Sig Figs

Sig Fig Rules All non-zero digits are significant All zeros between non-zero digits are significant. All beginning zeros are NOT significant. Ending zeros are significant if the decimal point is actually written in but not significant if the decimal point is an understood decimal. Ex. 567845656 cm – 9 sig figs Ex. 560005 cm – 6 sig figs Ex. 0.00000567 cm – 3 sig figs Ex. 26000. g 26000.0 g 26000 g – 5 sig figs -- 6 sig figs -- 2 sig figs

Try the following: How many significant figures are in each of the following measurements? A. 28.6 g B. 3440. cm C. 910 m D. 0.046 04 L E. 0.006 700 0 kg 3 4 2 4 5

Round 2 on worksheet Answers: 500,000 = 1 5,000.0 = 5 104 = 3 0.0021 = 2 0.3350 = 4 8.0110 x 107 = 5

Addition and subtraction rule Round your answer to the lowest number of decimal places!!! Let’s think why this is the rule, When you are adding and subtracting sometimes the values can change a lot in size, if you needed to add on just a small measurement it would not change the precision (it’s just a small number but it only has 1 sig fig)

Adding or Subtracting with SigFigs Round off the calculated result to the same number of decimal places as the measurement with the fewest decimal places. 

Multiplication and Division Rule Round your answer to the lowest number of significant figures Let’s think why this is the rule, The number itself no longer expresses a measurement it becomes two measurements combined--grams per milliliter--so it has turned into just a number; therefore, to reflect precision we look at the precision of the measurements using sig figs and base the calculated value on the least precise measurement.

Multiplying or Dividing with Significant Figures For multiplication or division the answer can have no more significant figures than are in the measurement with the FEWEST significant figures

EXAMPLE PROBLEMS A. 5.44 m – 2.6103 m = B. 2.4 g/mL x 15.82 mL = C. What is the sum of 2.099 and 0.05681 g? D. Calculate the area of a crystal surface that measures 1.34 micrometers by 0.7488 micrometers 2.8297 = 2.83 m 37.968= 38 g 2.15571 = 2.156 g 1.34 µm x 0.7488 µm = 1.003392 = 1.00 µm2

Round 3 on Worksheet Answers: 5.88g/mL x 7.65 mL = 45.0g 81.5g / 2.54 mL = 32.1 g/mL 12.3m + 0.23m = 12.5m 158 mL – 15.9 mL = 142 mL

Best Practice: Always use the most precise glassware Let me prove this to you with some examples

#1: same precision, same sig figs 5.111 g / 1.633 mL = ??? calculator value 3.12982241 3.130 g/mL This is the best case Both numbers are precise to the thousandths place and have 4 sig figs

#2 Same Precision, Different Sig figs This happens a lot especially if you are looking at two measurements that are different by a factor of 10 1.0123 g / 0.323 = mL = ???? 3.13405573 3.13 g/mL (this is the same material from #1, look at what happened to our density it went from 3.130 g/mL to 3.13 g/mL) Helpful hint! Try your best to use glassware that is the appropriate size if measuring 5 mL use 10 mL graduated cylinder vs a 25 mL graduated cylinder, both grad cylinders have the same number of markings, but the 10 mL is smaller, the smaller increments are in the hundredths place! Whereas the 25 mL smallest increments are in the ones place.

#3 different sig figs and different precision 10.123 g / 3.2 mL = ??? calculated value 3.1634375 3.2 g/mL yuck! density went from 3.160 g/mL to 3.16 g/mL to 3.2 g/mL This shows how using less precise glassware leads to less Accurate answers

Questions?

Assignment Significant Figures

Thursday, October 1, 2015 Convert 3.4 m3 to cm3 How many cm are in 234,256 mm? Convert 9584 cm of copper wire to m.

Thursday, October 1, 2015 Convert 3.4 m3 to cm3 3.4 x 100 x 100 x 100 = 3,400,000 cm3 How many cm are in 234,256 mm? 234,256 / 10 = 23425.6 cm Convert 9584 cm of copper wire to m. 9584 / 100 = 95.84 m

Rounding If the digit following the last digit to be retained is: Then the last digit should: Example: (rounded to 3 sig figs) Greater than 5 Be increased by 1 42.68 g 42.7 g Less than 5 Stay the same 17.32 m 17.3 m 5 followed by nonzero digits 2.7851 cm  2.79 cm 5, not followed by nonzero digits and preceded by an odd digit 4.635 kg  4.64 kg (because 3 is odd) 5, not followed by nonzero digits and the preceding sig fig is even 78.65 mL 78.6 mL (because 6 is even)