2 Standards & Objectives MA.912.S.1.2—Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment.Objectives:Distinguish between Accuracy and PrecisionDetermine the number of significant figures in a measurement.Read and record measurements with the correct number of significant figures.
3 Identify the following as accurate or precise. Key WordDefinitionExampleAccuracy the closeness of a measurement to the true or accepted valueHitting the Bullseye on the dartboardPrecisionagreement among a set of measurements made of the same quantity in the same way.(repeatability or consistency)Hitting the same spot with darts the same time.Identify the following as accurate or precise.
4 Not accurate or precise. Accurate and precise Not accurate or precise.Accurate and precisePrecise but not accurate.*Same spot but not on the bullseye
5 Accuracy and Precision Carpenter 1Measurement 147.5 cmMeasurement 246.8 cmMeasurement 345.3 cmCarpenter 2Measurement 147.0 cmMeasurement 247.1 cmMeasurement 346.9 cmIf the window measures 47 cm exactlyAre the measurements accurate/precise?
6 Accuracy and Precision Carpenter 1Measurement 147.5 cmMeasurement 246.8 cmMeasurement 345.3 cmCarpenter 2Measurement 147.0 cmMeasurement 247.1 cmMeasurement 346.9 cmIf the window measures 47 cm exactlyAre the measurements accurate/precise?Carpenter 1: has measurement’s with great variety.Neither accurate or precise.Carpenter 2: precise, accurate if the true length is around 47.0 cm.
7 How do you measure accurately and precisely? Significant FiguresSuppose you were asked to measure the length of a pencil using a ruler in cm?How do you measure accurately and precisely?
8 Why use Significant Figures? I might say 6.7, you might say 6.8, your friend might say 6.75 cm. Who is right? How do we show consistency in the way all scientists read and record measurements?
9 Significant Figures Keyword Definition Example Significant Figure All digits in a measurement that are known with certainty plus one final digit that is estimated and uncertain.See Rules for significant figure examples.GraduationA line that marks a measurement, (dash marks on a rule or graduated cylinder)Example below
10 Use significant figures (sig figs for short) in 3 ways: What is a Sig Fig?Use significant figures (sig figs for short) in 3 ways:1. You will make measurements and report them to others. Determine the number of sig figs by estimating one digit past the smallest measurement, or graduation, on the measuring tool.
11 What is a Sig Fig?Ex. 1: The graduations go in 10 degree increments. So, you can know the temperature for certain to the tens place and can estimate in the ones place. Estimate that the temperature is 6°C, 7°C, 8°.Ex. 2: The graduations on this thermometer mark off every one degree. You can measure the temperature to the ones place for certain and can estimate to the tenths place. You may read this thermometer as 3.6°C, 3.7°C, 3.8°.Ex 3: The graduations on this thermometer mark off every tenth of a degree (o.1 increments). You can know the temperature to the tenths place for certain and can estimate to the hundredths place. You may have read this temperature as 0.69°C, 0.70°C, 0.71°.
12 What is a Sig Fig?2. You will interpret the measurements reported by others. Data provided will show the instrument used because you know that scientists always estimate one digit past the smallest graduation on a measuring tool. 3. You will need to keep track of sig figs when measurements are used in calculations. You must have correct values in measurement to use correct # of sig figs in calculations.
14 Significant Figures Example Answer Explanation 22.51 g 0.076 g 200 mL 2.20 x 10^-3 g
15 Significant Figures Example Answer Explanation 22.51 g 4 Sig Figs Rule 1 All nonzero numbers are significant0.076 g2 Sig FigsRule 3 Zero’s to the left are not significant200 mL1 Sig FigRule 4 Zero’s at the end only count of there is a decimal250.0 mLRule 4 Zero’s at the end count only if there is a decimal2.20 x 10^-3 g3 Sig FigsRule 5 all digits of a coefficient in scientific notation count .
16 Sig Figs in Calculations The results of the calculations are not allowed to appear more or less accurate than the original measurements used. Follow simple rules when multiplying, dividing, adding, or subtracting helps make sure that all results are represented with the appropriate amount of reliability.
17 Rules for Multiplication/Division Only given measurements affect the number of sig figs allowed in the final answer. Conversion factors or equivalences don’t affect it. (Ex: 1 m= 1000 mm)If you are only given one measurement, the total number of sig figs in that measurement equal the total number of sig figs allowed in your final answer.If you are given more than one measurement, the final answer must be rounded to the same total number of sig figs as the measurement that has the least.
18 Rules for Multiplication/Division Example problemsConvert 72.0 cm to the unit dam.Calculate the density of an object that has a mass of g and a volume of 64.0 mL.
19 Rules for Multiplication/Division Example problemsConvert 72.0 cm to the unit dam.Calculate the density of an object that has a mass of g and a volume of 64.0 mL.D = mass / volumeDensity = g / 64.0 mLDensity = g / mL**Round to 3 sig figs b/c 64.0 mL only has 3Final answer 1.63 g /mL10^-2 m1 dam72.0 cm= dam1 cm10^1 mNote the 3 sig figs for #1, 720….not the zero’s at beginning.
20 Rules for Addition/Subtraction The final answer cannot have more places after the decimal than any of the given measurements.The final answer cannot have a final digit, which represents the uncertain or estimated place, farther to the right than any of the final digits in the measurements used.
21 Rules for Addition/Subtraction Example problemsAdd 101.5g gSubtract 101.5g g
22 Rules for Addition/Subtraction Example problemsAdd 101.5g g= gActual answer w/ correct Sig Figs can only have 1 place after decimal.28.4 g2. Subtract 101.5g g83.64 g , Actual answer can only have 1 place after decimal83.6 g
23 Rules for Rounding up or down It is sometimes necessary to round your answer or add zeros to the end of the answer to give it the proper number of sig figs.
24 Rules for Rounding up or down Example problemsCalculate the density of an object that has a mass of g and a volume of 49.5 mL.Density = mass/ volumeDensity = g / 49.5 mLDensity = g/mLFinal answer can only have 1 place after decimal and no more than 3 sig figs, whatever is less. Round down.** 2.0 g/mLIf a beaker containing a sample of powder has a mass of and the clean, empty beaker has a mass of grams, what is the mass of the powder?65.09 – g = 10.4 g but must round to 2 decimals places after decimal, so add a zero.**10.40 g