Reliability of Measurements

Chapter 2.3

Objectives

I can define and compare accuracy and precision.

I can calculate percent error to describe the accuracy of experimental data.

I can use significant figures and rounding to reflect the certainty of data.

Accuracy and Precision

Often accuracy and precision confused for one another, but they are different concepts.

ACCURACY

How close the measured value is to the accepted value

Ex: How close to the center of the dart board?

PRECISIONHow close a series of measurements are to

one another

Ex: How close together are all the darts you throw together?

If you took another measurement, how close would it be to the others?

Accuracy and Precision

What are the precision and accuracy levels of the following?

Low Accuracy High Accuracy Low Accuracy High Precision High Precision Low Precision

Whose data is most accurate/precise?

Three chemistry students measured the mass and volume of a piece of zinc to determine it’s density.

The table below shows the data:

John Sam Sara

Trial 1 7.17 g/mL 7.65 g/mL 7.04 g/mL

Trial 2 7.14 g/mL 7.65 g/mL 7.55 g/mL

Trial 3 7.13 g/mL 7.64 g/mL 7.26 g/mL

Average 7.15 g/mL 7.65 g/mL 7.28 g/mL

Compare the students data.

Whose data is the most accurate and precise?

Percent Error

A way to evaluate the accuracy of data.

Percent Error=Ratio of the error to the accepted value

│Accepted value – Measured value │Accepted value X 100%

Percent Error

If your measurement of a liquid is 123.4 mL but the actual amount is 125.0 mL, what is the percent error of the

measurement?

125.0 mL – 123.4 mL 1.6 mL________________________________________ _______________

125.0 mL 125.0 mL = X 100% = 1.3%

Percent Deviation

A way to evaluate the precision of the data.

Percent Deviation=Ratio of your measurements change from the average compared to the average value

│Mean value – Measured value │Mean value X 100%

Percent Deviation

If one of your measurements of the length of a string was 22.7 cm and the

mean measurement was 22.9 cm, what is the percent deviation of the

measurement?22.9 cm – 22.7 cm 0.2 cm________________________________________ _______________

22.9 cm 22.9 cm = X 100% = 0.9%

Significant Figures

The number of digits reported in a measurement.

All the known digits plus one estimated value.

The number of significant figures possible depends upon the piece of equipment used to take the measurement.

Significant Figures

Rules for Significant Figures1. Non-zero numbers are always significant.2. Zeros between non-zeros are always

significant.3. All final zeros to the right of the decimal

place are significant. 4. Zeros that act as placeholders are NOT

significant. 5. Counting numbers and defined constants

have an infinite number of significant figures.

Practicing Significant FiguresDetermine the number of sig figs in the following numbers.

1)0.02

2)70001

3)5600

4)4.100

5)3.1416

(π)

6)2.80 x

105

0.02

70001

5600

4.100

3.1416 (π)

2.80 x 105

1

5

2

4

Infinite

3

Red numbers=significant Black numbers=not significant

Rules for Rounding

If the digit to the immediate right of the last sig fig is 5-9, round up.

If not, leave as is.

Significant Figures and Calculators

When using a calculator, you should do the calculation using the digits allowed by the calculator and round off only at

the end of the problem.

Do not round off in the middle of the problem!

Sig Figs and Addition/Subtraction

+ - + - + - + - + - + - + - +When you add or subtract, you answer must have the same number of digits to

the right of the decimal point as the original value with the fewest digits to

the right of the decimal place.+ - + - + - + - + - + - + - +

Sig Figs and Multiplication/Division

When you multiply or divide, your ansere must have the same number of significant figures as the original value

with the least significant figures.

Practicing Significant Figures

3.33 m2

25 m

53 mL

26.6 g

6.7 cm3