1.07 Accuracy and Precision

My Goals for this Lesson:

·  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.

I’m preparing to complete a lab on Accuracy and Precision

Measurements must include an indication of its uncertainty or reliability. This lesson discusses how measurements are reported and used.

Learn About Accuracy and Precision

______ is the closeness of a measurement to the ______or accepted value.

______ refers to the ______among a set of measurements made of the same quantity in the same way, or ______.

Suppose the new guy on the crew measured the width of the opening three times and got the measurements:

These values have ______, because These values have ______,

they are ______. they ______.

470cm is the ______or ______.

These values are

Random error and

No error and

Systematic error

Watch the video Measuring and recording data

http://streaming.discoveryeducation.com/index.cfm?guidAssetId=B29DB0D2-0316-4AC8-BB55-DFBDB77A938E

When you ______with a ruler, a thermometer, or a balance, you are ______by the precision of the instrument and you must use the ______properly and read the ______carefully.

Lab measurements should be recorded. A _____ is a convenient way to ______your _____.

To indicate the precision of a measurement, we use ______. These are all the numbers that can be read from an ______—like a ruler, a thermometer, or a balance—and one ______number. The more significant digits, the more precise the measurement.

Significant Digits

When ______a defined ______with a ruler, there is a source of _____ and the measurement may need ______or rounding between two points. When doing this estimation, it is possible to ______or ______the measured value, meaning there is a possibility for ______.

Here is a pencil whose length lies between ___ and ____. With an intermediate mark, the ruler shows in greater detail that the pencil length lies somewhere between ____ and _____. Therefore, one may reasonably approximate that the length of the pencil is _____.

How long is it? The end of the pencil is between the seventh and eighth mark. The third digit in the measurement must be estimated: 6.73 cm

The significant figures in a measurement include all the digits known with certainty plus one final digit that is estimated and uncertain.

Estimating the final digit

The graduations on this thermometer go in 10 degree increments, estimate the ones place. The temperature is 6°C, 7°C or 8°C. / The graduations on this thermometer mark off every one degree and can estimate to the tenths place: 3.6°C, 3.7°C or 3.8°C. / The graduations on this thermometer mark off every tenth of a degree and can estimate to the hundredths place: 0.69°C, 0.70°C or 0.71°C.

Determining significant figures

Determining the significant digits in the measurement 12.34 g is easy; just count the total number of digits. This number has four sig figs.

When a number includes zeroes, like 0.00450 L or 270 m, some additional rules are needed for determining the sig figs.

Review Significant Figures—Rules and Practice – Text only version

Practice - Determine the number of significant digits in each of the measurements below.

1 - 203 cg , 2 - 0.001710° C, 3 - 80 mm, 4 - 0.0530 g, 5- 2.700 × 105 L

Significant figures in Calculations

After taking measurements, sometimes scientists need to use those measurements in ______. These calculations may include ______several measurements together or ______mass by volume to get the density of an object. The results of the calculations are not ______to appear more or less accurate than the ______used.

For ______and ______, the answer should be rounded off to the same number of total ______as in the measurement with the ______significant figures.

For ______and ______, the answer should be rounded off so that the number of ______is the same as in the measurement with the ______decimals.

In order to follow the significant figures rules for calculations, it is sometimes necessary to round your answer or add zeros to the end of the answer to give it the proper number of significant figures.

Complete the examples

Now it is time to try some calculations on your own. Calculate the answer to each question and enter it below. Remember to round your answer to the correct number of sig figs.

Question 1: 6.821 m + 1.4 m + 1.05 m =

Question 2:26.50 g ÷ 9.67 mL =

Question 3: Convert 17.8 m/s to the unit km/hr

Question 4:12.50 Kg — 17.80 Kg + 13.0 Kg =

Complete the Measuring Lab

Use the lab worksheet provided at the end of these notes. Copy and paste it into a new document.

Measurement is an important skill used for data collection and data analysis. Careful attention to the accuracy and degree of uncertainty of each measuring device is necessary for proper data collection. Significant figures are used to record or report measurements accurately.

01.07 Accuracy and Precision: Balance Lab Worksheet

Measurement

·  Measurement is an important skill used for data collection and data analysis. Careful attention to the accuracy and degree of uncertainty of each measuring device is necessary for proper data collection. Significant figures are used to record or report measurements accurately.

·  This laboratory activity will give you the opportunity to get more familiar with some of the basic measuring devices that are common in chemistry labs. You will use the measurements performed in this lab to calculate density.

Procedure

·  Access the virtual lab and complete the experiments.

Data

·  Below is the table that you will complete for the virtual lab. Either type your results into this table or print the table from the virtual lab (it must be submitted to receive full credit for this assignment.)

·  To print from the virtual lab.

1.  Be sure the data table is viewable.

2.  Right-click (PC) or Command-Click (Mac) on the table and select print.

Part I: Density of Unknown Liquid
Trial1 / Trial2 / Trial3
Measure Mass of Empty 10 mL graduated cylinder (g)
Measure Volume of liquid (mL)
Measure Mass of graduated cylinder and liquid (g)
Calculate the mass of the liquid for each trial
Calculate the density of the unknown liquid for each trial
Average
Part II: Density of Irregular-Shaped Solid
Trial1 / Trial2 / Trial3
Measure Mass of solid (g)
Measure Volume of water (milliliters)
Measure Volume of water and solid (milliliters)
Calculate the volume of the irregular-shaped solid for each trial
Calculate the density of the irregular-shaped solid for each trial
Average
Part III: Density of Regular-Shaped Solid
Trial1 / Trial2 / Trial3
Measure Mass of solid (grams)
Measure Length of solid (centimeters)
Measure Width of solid (centimeters)
Measure Height of solid (centimeters)
Calculate the volume of the regular shaped solid for each trial
Calculate the density of the regular-shaped solid for each trial
Average

Calculations

Show all of your work for each of the following calculations and be careful to follow significant figure rules in each calculation.

Part I: Density of Unknown Liquid

1.  Calculate the mass of the liquid for each trial. (Subtract the mass of the empty graduated cylinder from the mass of the graduated cylinder with liquid.)

§  Trial 1

§  Trial 2

§  Trial 3

2.  Calculate the density of the unknown liquid for each trial. (Divide the mass of the liquid calculated above by the volume of the liquid.)

§  Trial 1:

§  Trial 2:

§  Trial 3:

Part II: Density of Irregular-Shaped Solid

3.  Calculate the volume of the irregular-shaped solid for each trial. (Subtract the volume of the water from the total volume of the water and solid.)

§  Trial 1:

§  Trial 2:

§  Trial 3:

4.  Calculate the density of the irregular-shaped solid for each trial. (Divide the mass of the solid by the volume of the solid calculated above.)

§  Trial 1:

§  Trial 2:

§  Trial 3:

Part III: Density of Regular-Shaped Solid

5.  Calculate the volume of the regular shaped solid for each trial.
(Multiply the length × width × height for each trial to get the volume in the unit cm3.)

§  Trial 1:

§  Trial 2:

§  Trial 3:

6.  Calculate the density of the regular-shaped solid for each trial. (Divide the mass of the solid by the volume calculated above.)

§  Trial 1:

§  Trial 2:

§  Trial 3:

Questions and Conclusions:

1.  How would you determine the proper number of significant figures of a liquid using a graduated cylinder?

2.  Can just one measurement be considered precise? Can just one measurement be considered accurate? Explain your answers completely.

3.  In parts II and III of the lab you used different sized objects in each trial. Compare the density values that you calculated for these items, how do the three trials compare?