SIGNIFICANT FIGURES
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Imagine you are asked to measure the length of something...
and someone hands you this.
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How do we use it most effectively?
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Rulers, thermometers, and graduated cylinders, to name a few, are pieces of
equipment used to measure. In this activity, you will explore several methods for
accurately and precisely measuring quantities and doing so using significant figures.
Be sure to use your notebook to record your calculations and observations.
GET STARTED
COMPONENTS OF SIGNIFICANT FIGURES
ACCURACY &
PRECISION
MEASURING WITH
SIGNIFICANT FIGURES
VOLUME OF
LIQUIDS
PERCENT ERROR LENGTH
WHY ARE THEY
SIGNIFICANT?
CLICK HERE WHEN YOU HAVE EXPLORED THE LINKS ABOVE
1. ACCURACY & PRECISION
Accuracy: How close to perfect you are.
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Precision: How repeatable your data is.
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Each of five students used the same ruler to measure the length of the same pencil. The resultant data: 15.33 cm, 15.34 cm, 15.33 cm, 15.33 cm, and 15.34 cm. The actual length of the pencil was 15.85 cm.
Describe whether the Accuracy and Precision are each good or poor for these measurements.
PERCENT ERROR
A chemistry student measured the boiling point of naphthalene (C10H8) at 231.0˚C. What is the percent error for this measurement if the literature value is 217.9˚C?
*Remember to use the ESA method for solving this problem.
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2. MEASURING WITH SIG FIGS
Significant figures are important because they tell us how good the data
we are using are.*
NEXT*The word “data” is plural for “datum”, so even though it seems weird saying that “data are [something]”, it’s grammatically correct.
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TEMPERATUREMake measurements using the pictures on each slide.
Show the correct number of significant figures.
Lab: Sig Figs
Purpose: To investigate how to improve
precision with different measuring instruments
and use of significant figures.
Safety: None
Station 1 – Accuracy & Precision
1. Each of five students used the same ruler to
measure the length of the same pencil. These data
resulted: 15.33 cm, 15.34 cm, 15.33 cm, 15.33 cm,
15.34 cm. The actual length of the pencil was 15.85 cm. Describe whether accuracy and precision are
each good or poor for these measurements.
2. A chemistry student measured the boiling point of naphthalene (C10H8) at 231.0°C. What is the percent
error for this measurement if the literature value is 217.9°C?
Station 2 – Measuring with Sig Figs
Make measurements use the pictures on the right.
Show the correct number of significant figures.
3. ________________ Temperature in oC (close up of thermometer)
4. ________________ Volume in mL (graduated cylinder)
5. ________________ Length of line in cm (ruler)
________ Temperature in ˚C (close up of thermometer)
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VOLUME
________ Volume in mL (graduated cylinder)
Lab: Sig Figs
Purpose: To investigate how to improve
precision with different measuring instruments
and use of significant figures.
Safety: None
Station 1 – Accuracy & Precision
1. Each of five students used the same ruler to
measure the length of the same pencil. These data
resulted: 15.33 cm, 15.34 cm, 15.33 cm, 15.33 cm,
15.34 cm. The actual length of the pencil was 15.85 cm. Describe whether accuracy and precision are
each good or poor for these measurements.
2. A chemistry student measured the boiling point of naphthalene (C10H8) at 231.0°C. What is the percent
error for this measurement if the literature value is 217.9°C?
Station 2 – Measuring with Sig Figs
Make measurements use the pictures on the right.
Show the correct number of significant figures.
3. ________________ Temperature in oC (close up of thermometer)
4. ________________ Volume in mL (graduated cylinder)
5. ________________ Length of line in cm (ruler)
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LENGTH
________ Length of line in cm (ruler)
Lab: Sig Figs
Purpose: To investigate how to improve
precision with different measuring instruments
and use of significant figures.
Safety: None
Station 1 – Accuracy & Precision
1. Each of five students used the same ruler to
measure the length of the same pencil. These data
resulted: 15.33 cm, 15.34 cm, 15.33 cm, 15.33 cm,
15.34 cm. The actual length of the pencil was 15.85 cm. Describe whether accuracy and precision are
each good or poor for these measurements.
2. A chemistry student measured the boiling point of naphthalene (C10H8) at 231.0°C. What is the percent
error for this measurement if the literature value is 217.9°C?
Station 2 – Measuring with Sig Figs
Make measurements use the pictures on the right.
Show the correct number of significant figures.
3. ________________ Temperature in oC (close up of thermometer)
4. ________________ Volume in mL (graduated cylinder)
5. ________________ Length of line in cm (ruler)
3. VOLUME OF LIQUIDSDirections: • Measure 25 mL of water into a beaker. • Measure and record the volume, being careful to report your data
to the correct number of significant figures and units. • Pour that SAME liquid into the following measuring instruments,
being careful to follow this order: 100 mL graduated cylinder, 50 mL graduated cylinder, 10 mL graduated cylinders.
• Record each of your measurements to the correct number of sig figs and units.
• Compare your measurements with two other sets of partners and answer the analysis questions.
• Duplicate the table on the next slide to record your data
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VOLUME
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TESTINGYour Data Group #1 Data Group #2 Data
Beaker
100 mL graduated cylinder
50 mL graduated cylinder
10 mL graduated cylinders (total the
volumes)
ANALYSIS QUESTIONS
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1. Can you report all of your measurements to the same number of significant figures? Explain your answer using your knowledge of significant figures.
2. Are your measurements precise? Explain your answer using your data as support.
Answer the following questions in your notebook.
ANALYSIS QUESTIONS
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3. Which piece of glassware do you believe was most accurate? Use your data to support your answer.
4. Which type of glassware would best measure 2.5 mL of water? Explain.
Answer the following questions in your notebook.
4. PERCENT ERRORThe amount of error associated with a
measurement compared to a known value.
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PERCENT ERROR
Reference Tables for Physical Setting/Chemistry – 2011 Edition 12
Table TImportant Formulas and Equations
DET 609 ADU
d = densityDensity d = m = mass
V = volume
Mole Calculations number of moles =
Percent Error % error = × 100
Percent Composition % composition by mass = × 100
parts per million = × 1000000
Concentration
molarity =
P = pressureCombined Gas Law = V = volume
T = temperature
MA = molarity of H+ MB = molarity of OH–
Titration MAVA = MBVB VA = volume of acid VB = volume of base
q = mC∆T q = heat Hf = heat of fusionHeat q = mHf m = mass Hv = heat of vaporization
q = mHv C = specific heat capacity ∆T = change in temperature
Temperature K = °C + 273 K = kelvin°C = degree Celsius
P2V2T2
P1V1T1
moles of soluteliter of solution
mass of solutemass of solution
mass of partmass of whole
measured value – accepted valueaccepted value
given massgram-formula mass
mV
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PERCENT ERRORDirections: With a partner, measure your height and arm span. Both you and your partner need to complete the measurements for question 1 (you will each record the data from your own height and arm span). Include units and show all work during calculations.
Your Height:______________________
Your Total Arm Span (from finger tip to finger tip): ________________________
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ANALYSIS QUESTIONS1.In studying the human body, the Greeks
discovered a person’s height is nearly the same as their total arm span. Were the Greeks correct? Calculate the percent difference between your height and your arm span.
2.Identify at least one possible experimental (NOT human) error that could have occurred during this activity. How will this error alter your percent difference calculated in question 1.
5. LENGTHDirections: Using your metric ruler, measure the objects found at your station. Report your values
to proper significant figures and with proper units. Duplicate the table on the following slide.
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LENGTHObject Length
Height of your Lab Bench (or table)
Length of line (on index card)
Diameter of the Circle (on the index card)
Thickness of a Paper Clip
Length of String
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ANALYSIS QUESTIONS
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1.Did you encounter any problems when measuring your objects?
2.Do you think your measurements are accurate? Explain why or why not.
3.Did the ruler provide you with an appropriate scale to measure all of the objects?
6. WHY ARE THEY SIGNIFICANT?
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Determine the number of significant figures in each of the following. EXPLAIN your reasoning.
Sig Figs - Why?
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NumberNumber of
Sig FigsReason
3.57 m
20.040 g
0.004 m3
730,000 kg
12,700. mL
30 atoms
0.6034 g/mL
19.0 s
810˚C
0.0100 mol
Keep in mind...
Significant Figures are important for scientists and statisticians to
keep track of when taking measurements. The numbers
truly have meaning!
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Nice work! Now complete your Lab Credit
Sheet (LCS) for this lab and then...
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You’re Done!
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