• Quality of Data

• Precision:

• Well-grouped together

• Results are repeatable

• Compare to other repeated measurements

• Accuracy:

• Close to actual value

• Compare to correct value

Accuracy v. Precision

Accuracy v. Precision

Not accurate – the hits are not close to bulls eye

Not precise – none of the hits are close togetherNot accurate – none of the hits are close to

bulls eye

Precise – all the hits are close togetherAccurate – all the hits are near the bulls eye

Precise – all the hits are close togetherPrecise – all the hits are close together

2 ways to show 2 ways to show accuracy & precisionaccuracy & precision

Significant FiguresPercent Error

• Significant Figures : numbers that show precision in measurements

• Key question: Is there a decimal?

YES: come from left, 1st number (non-zero) and anything after it is significant

0.001 ml 4.7200 mL 82.0 sec

Accuracy with Measurements

Accuracy with Measurements

• Significant Figures

• Practice: http://science.widener.edu/svb/tutorial/sigfigures.html

• Rounding to Significant Figures

314.721 (four) 0.001775 (two)

8792 (two) 4.3622x10-5 (three)

87.073 (three) 1040 (two)

Accuracy with Measurements

314.7

8800

87.1

0.00184.36x10-5

1.0x103

• Practical Applications: Estimating in Measurements

• Always estimate one decimal place past the actual accuracy of the measuring device’s scale

Accuracy with Measurements

• Practical Applications: Estimating in MeasurementsAccuracy with Measurements

• Significant Figures in Calculations

• Multiplication and Division

• Answer’s sig figs = least sig figs

• Example: 3.126x10-6 x 2.8x10-7 =

8.8x10-

13

Accuracy with Measurements

• Practice!

Accuracy with Measurements

Use your calculator to find the following answers. Report it in scientific notation. Round to the proper amount of sig figs

1)5.231 x 10-4 ÷ 1.49 x 104 =2)9.62 x 105 x 5.4 x 106 =3)2.62x10-4 ÷ 3.14x10-8 =4)7.72x10-2 x 5.74x10-2 =5)8.22x10-5 ÷ 3 x104 =

3.51x10-

85.2x1012

8344.00443

1

= 8.34x103

3x10-9

= 4.43x10-

3

Accuracy with Measurements

• Practice!

Accuracy with Measurements

Use your calculator to find the following answers. Report it in scientific notation. Round to the proper amount of sig figs

1)39.64 + 1.3 = 2)195.4 – 193 = 3)5.8465x102 + 1.2x103 = 4)9x102 + 5x102 = 5)46.8 – 41.4 =

40.92

1.8x103

1.4x103

5.4

WebAssign HintWebAssign Hint• Just assume that you should use sig figs from here on

out. Also, on the WebAssign, you will see this:

This symbol means you must put the correct number of significant figures on web assign (not always 4)

• Percent error: shows how accurate experimental values are by determining how much error they have

Data Analysis

Actual = correct answer

Experimental = what you got

• Practice: The density of silver is 10.49 g/ml. If I measured it to be 11.1 g/ml, what is my percent error?

Data Analysis

5.82% error

• Practice: The density of gold is 19.32 g/cm3. What is the percent error of the following experimental measurements?

a) 20.1 g/cm3 c) 19.7 g/cm3

b) 19.51 g/cm3 d) 18.90 g/cm3

Data Analysis

4.04 % error

0.9834 % error

1.97 % error

2.174 % error

• Practice Problems

Accuracy with Measurements

Due tomorrow