Accuracy

& Precision

Measurement vs. Number

Significant Digits and Accuracy• Exact numbers – number determined by

counting or definition

1 2 3 4

• Approximate numbers – number determined by measurement or estimation

Accuracy• Accuracy – number

of digits we are reasonably sure of having counted (all certain digits + 1st uncertain)

• Called significant digits

• The greater the number of significant digits, the better the accuracy

For our graduated cylinder, accuracy is to 3

significant digits

1

2

3

Accuracy/Sig Fig Example

These divisions were visualized

Reading is between 2.8 cm & 2.9 cm

2.85 cm is measurement

“5” is uncertain

Significant Figures• Includes all numbers recorded in a measurement

For pin, length = 2.85 cm: 3 significant figures All certain numbers plus first uncertain

• Assume to be accurate to ± 1 in last # Pin length is 2.85 ±

0.01 cm Pin is somewhere

between 2.84 & 2.86 cm

Accuracy & Sig Figs

All of the following have 2 significant figures

386 3.86 38.6 0.3860.0386 38600 3860 386000

All of the following have 3 significant figures

41 4.1 0.41 0.041410 4100 41000 410000

Precision• Precision – smallest unit with which

measurement is made, or the position of the last significant digit

• Try not to confuse accuracy and precision (often have similar meanings)

Which measuring

instrument is more

precise?

Precision of Numbers

All of the following are precise to 0.010.52 5.20 52.00 52.02 520.000.05 0.02 25.20 25.02 2.05

All of the following are precise to 100

5200 200 500 52500 50500123500 1200 4500 600 98700

Accuracy vs. Precision

Which Number is most Precise?

863 8.63 86.3

Which Number is most Accurate?

8 8.6 86.3

Accuracy & Precision of DataReplicates Results

1 10.282 10.223 9.814 9.755 10.366 9.767 10.118 9.869 10.25

10 9.86Average 10.03Standard Deviation 0.24

True Value = 10.00

Accuracy = Good (Average = 10.03)

Precision = Bad(Std Dev = 0.24)

Accuracy & Precision of DataReplicates Results

1 10.562 10.513 10.554 10.495 10.366 10.597 10.388 10.609 10.59

10 10.53Average 10.52Standard Deviation 0.08

True Value = 10.00

Accuracy = Bad(Average = 10.52)

Precision = Good(Std Dev = 0.08)

Accuracy & Precision of DataReplicates Results

1 10.032 10.053 9.974 10.015 10.116 9.957 9.988 10.029 9.96

10 10.03Average 10.01Standard Deviation 0.04

True Value = 10.00

Accuracy = Good(Average = 10.01)

Precision = Good(Std Dev = 0.04)