Accuracy, Precision and Significant Figures. Significant Figures. Accuracy: Significant Figures: Precision: Summary: Accuracy & Precision

Accuracy:  Accuracy, Precision and Significant Figures   This is the concept which deals with whether a measurement is correct when compared to...
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Accuracy: 

Accuracy, Precision and Significant Figures





This is the concept which deals with whether a measurement is correct when compared to the known value or standard for that particular measurement. When a statement about accuracy is made, it often involves a statement about percent error. error. Percent error is often expressed by the following equation: Actual − Experiemental % error =

Precision: 

This is the concept which addresses the degree of

exactness when expressing a particular measurement. 

The precision of any single measurement that is made by an observer is limited by how precise the tool (measuring instrument) is in terms of its smallest unit.

Experimental

× 100

Significant Figures: 





When someone else has made a measurement, you have no control over the choice of the measuring tool or the degree of precision associated with the device used. You must rely on a set of rules to tell you the degree of precision. Refer to the “Tutorial: Significant Figures, Precision, and Accuracy ” Handout (later)

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Summary: Accuracy & Precision Accuracy refers to how “correct” a measurement is; how close it is to the accepted value. Precision refers to how exactly a measurement is reported; or how closely repeated measurements will agree. A measurement can be precise, but inaccurate. A measurement can be imprecise, but accurate. Examples: Balances Kilogram bathroom scale. Decigram balance. Centigram balance. Analytical balance.

Significant Figures Significant Figures are ones that have been accurately measured. Sample Problems: How many significant digits are in each of the following?

a. 903.2 b. 0.0090 c. 0.007 d. 0.02 e. 90.3 f. 0.090 0

g. h. i. j. k. l.

0.0080 70 900.0 99 0.049 5.0002

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Yep…More Practice Problems 3.0800 0.00418 7.09 x 10-5 91,600 0.003005 3.200 x10 9 250 780,000 0.0101 0.00800

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

5 3 3 3 4 4 2 2 3 3

What if I measured it? You will be expected to use the rules for significant figures… figures… in all your calculations… calculations… ….and in all of your measurements

Measurements 



No measurement is exact; there is always some uncertainty. There are always two parts to a measurement:  

Numerical part Unit/label

Measuring with a Meter Stick 







Meter Stick Example 1 

What length is indicated by the arrow?

• • • •

More than 4, less than 5. More than 0.5 but less than 0.6 Guess at 0.00 So, 4.50 cm.

We know the object is greater than 2 and less than 3. We know the object is greater than 0.8 and less than 0.9 We can also guess at one more place. So, I’ll guess 0.04 Final answer 2.84 cm.

Meter Stick Example 2 

What length is indicated by the arrow?

9.40 cm

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Measuring with a Thermometer

Meter Stick Example 3 

What length is indicated by the arrow? 



12.34 cm





Thermometer Example 1 

What is the temperature?

Thermometer Example 2 

Measuring with a Graduated Cylinder

Thermometer Example 3 What is the temperature?

What is the temperature?

21.8 °C

28.5 °C



What is the temperature? Greater than 15, but less than 16. Guess one place. So, 0.0 Final answer = 15.0 °C

 



36.0 °C  

What is the volume? Read to the bottom of the meniscus. Greater than 30, less than 31. Guess at one. So, 0.0 Answer 30.0 mL

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Graduated Cylinder Example 1 

Graduated Cylinder Example 2

What is the volume?



27.5 mL

4.28 mL

Multiplication and Division with Significant Figures

Graduated Cylinder Example 3 

What is the volume?

What is the volume? 

Rule: Your final answer cannot contain any more significant figures than the least precise measured number; the measured number with the fewest significant figures.

5.00 mL

Significant Figures: Multiplication and Division Round to least amount of significant figures 3.22 cm X 2.1 cm 6.762 cm The answer would then be 6.8cm 

Practice 1. 2. 3. 4. 5. 6.

8.6 2.5 x 3.42 = 14.0 3.10 x 4.520 = 3.0 x 10 1 2.33 x 6.085 x 2.1 = 114 (4.52 x 10-4) / (3.980 x 10-6) = 6.17 x 10 10 (3.4617 x 107) / (5.61 x 10-4) = 2 5 (2.34 x 10 )(0.012)(5.2345 x 10 ) = 1500000

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Adding and Subtracting with Significant Figures 



As always, the answer is never more precise than the numbers used in the math: you can never be more precise than the least precise measurement. In addition and subtraction, only look at the decimal portion of the number.

Adding and Subtracting with Significant Figures Rules: 1. Count the number of significant digits in the decimal portion of each measured number. 2. Round the answer to the LEAST number of places in the decimal portion.  Ex.

24.686 m

2.343 m + 3.21_m_ 30.239 m The correct answer is 30.24 m

Practice 3.461728 + 14.91 + 0.980001 + 5.2631 =

24.61

2.

23.1 + 4.77 + 125.39 + 3.581=

156.8

3.

22.101 – 0.9307=

21.170

4.

0.04216 – 0.0004134 =

0.04175

5.

564321 – 264321=

300000

1.

Practice Problems

Our Goals: Be able to…  Determine the number of sig figs in a measurement.  Round any measurement to a set number of sig figs.  Use scientific notation when necessary.

Practice Problems

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1 How many significant figures:

Our Goals: Be able to… 0.000556 1.008 6.57 x 106 500.

Determine the number of sig figs in a measurement.  Round any measurement to a set number of sig figs.  Use scientific notation when necessary. 

2 How many significant figures:

3 

65.002 650,000 0.00808

Round to 3 sig figs: 1.70065 g 8.555 x 1012 km

3 

Round to 3 sig figs:

3 

Round to 4 sig figs:

1.008 g

400,885,000 J

12.599 kg

12.0091

seconds

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3 

Round to 2 sig figs:

3 

Round to 2 sig figs:

687,000 ly

999.5 g

0.00509 g

0.00799

• Calculate the mass of 125.0 mL of liquid with a density of 0.956 g/mL

Calculate the mass of 12.50 mL of lead (density = 11.4 g/mL)

Calculate the density of 12 mL of liquid, the mass is 9.55 g

Calculate the volume of 5.260 kg of liquid (density = 1.559 g/mL)

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Convert 3752 cm to meters.

Convert 3.5 liters per day to milliliters per second .

If it takes 780.2 Joules to heat a sample of a material weighing 8.69 g from 20.0 °C to 30.0 °C, what is the specific heat of the material?

Convert 3752 cm to inches.

How much energy is required to heat 120.0 g of water from 12.0 °C to 25.0 °C? ( Specific Heat of Water = 4.18 J/goC )

• A sample of Lead was heated with 1.18 x 105 Joules, raising its temperature from 105.0 °C to 118.5 °C. Find the mass of the sample in kg. ( Specific Heat of Lead = 0.129 J/goC )

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Convert 25,600 calories per minute to Joules per second . (4.1840 J = 1 calorie )

Calculate the density of a 12cm x 3cm x 10cm cube that has a mass of 458.9 g

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