# 1.07 Accuracy and Precision

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1.07 Accuracy and Precision
Concepts

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 Precision Determine the number of significant figures in a measurement. Read and record measurements with the correct number of significant figures.

Identify the following as accurate or precise.
Key Word Definition Example Accuracy  the closeness of a measurement to the true or accepted value Hitting the Bullseye on the dartboard Precision agreement 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.

Not accurate or precise. Accurate and precise
Not accurate or precise. Accurate and precise Precise but not accurate. *Same spot but not on the bullseye

Accuracy and Precision
Carpenter 1 Measurement 1 47.5 cm Measurement 2 46.8 cm Measurement 3 45.3 cm Carpenter 2 Measurement 1 47.0 cm Measurement 2 47.1 cm Measurement 3 46.9 cm If the window measures 47 cm exactly Are the measurements accurate/precise?

Accuracy and Precision
Carpenter 1 Measurement 1 47.5 cm Measurement 2 46.8 cm Measurement 3 45.3 cm Carpenter 2 Measurement 1 47.0 cm Measurement 2 47.1 cm Measurement 3 46.9 cm If the window measures 47 cm exactly Are 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.

How do you measure accurately and precisely?
Significant Figures Suppose you were asked to measure the length of a pencil using a ruler in cm? How do you measure accurately and precisely?

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?

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. Graduation A line that marks a measurement, (dash marks on a rule or graduated cylinder) Example below

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.

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°.

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.

Rules to Determine Sig Figs

Significant Figures Example Answer Explanation 22.51 g 0.076 g 200 mL
2.20 x 10^-3 g

Significant Figures Example Answer Explanation 22.51 g 4 Sig Figs
Rule 1 All nonzero numbers are significant 0.076 g 2 Sig Figs Rule 3 Zero’s to the left are not significant 200 mL 1 Sig Fig Rule 4 Zero’s at the end only count of there is a decimal 250.0 mL Rule 4 Zero’s at the end count only if there is a decimal 2.20 x 10^-3 g 3 Sig Figs Rule 5 all digits of a coefficient in scientific notation count .

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.

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.

Rules for Multiplication/Division
Example problems Convert 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.

Rules for Multiplication/Division
Example problems Convert 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 / volume Density = g / 64.0 mL Density = g / mL **Round to 3 sig figs b/c 64.0 mL only has 3 Final answer 1.63 g /mL 10^-2 m 1 dam 72.0 cm = dam 1 cm 10^1 m Note the 3 sig figs for #1, 720….not the zero’s at beginning.

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.

Example problems Add 101.5g g Subtract 101.5g g

Example problems Add 101.5g g = g Actual answer w/ correct Sig Figs can only have 1 place after decimal. 28.4 g 2. Subtract 101.5g g 83.64 g , Actual answer can only have 1 place after decimal 83.6 g

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.

Rules for Rounding up or down
Example problems Calculate the density of an object that has a mass of g and a volume of 49.5 mL. Density = mass/ volume Density = g / 49.5 mL Density = g/mL Final answer can only have 1 place after decimal and no more than 3 sig figs, whatever is less. Round down. ** 2.0 g/mL If 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

Practice with Estimating Sig Figs

Practice with Estimating Sig Figs
89.9 mL 27.79 mL 54 mL

Practice with Estimating Sig Figs

Practice with Estimating Sig Figs
32.81 mL 55.8 mL 45 mL

What’s next? The Virtual Lab
Lab worksheet link: or go to the Chemistry Resource Center and click Blank Lab reports.