significant figures€¦ · and use of significant figures. safety: none station 1 – accuracy...

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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