What is the difference between accuracy and precision?

Good precisionLow accuracy

= average position

Low precisionHigh accuracy

Accuracy = how close to the true value a measurement is

Precision = (1) how close together the measurements are(2) how carefully a measurement has been made (# decimals)

Significant figures: represent the precision of a measurement

A 20 g weight is weighed on four different balances, and the four masses shown below were obtained. Which measurement is the most precise?

19.9 g 19.94 g 19.935 g 19.9351 g

19.9351 g is the most precise. It has the greatest number of significant figures.

# sig figs 3 4 5 6

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Determining the number of significant figures:

1. All nonzero figures are significant.

2. The only time zeros are NOT significant is when they precede nonzero numbers. They are merely placeholders.

#SigFigs?

1.15

101.5

0.015

Sci. Notation

0.00150

101.50

1.15 3

1.015 x 102 4

1.0150 x 102 5

1.5 x 10–2 2

1.50 x 10–3 3

Value

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Math with significant figures:

Addition/subtraction: line up the decimal points. The answer is rounded to the same number of decimal places as the value with the least number of decimal places.

28.0 cm

23.542 cm

25.64 cm+

77.2 cm

(77.182 cm)

Rounding Rules:

1. Round up if the next number is greater than 5.

2. Round down if the next number is less than 5.

3. If the next number is exactly 5, round up only if the number to be rounded is ODD.

Ex: 1.15 and 1.25 both round to 1.2

Rounding Rules:

1. Round up if the next number is greater than 5.

2. Round down if the next number is less than 5.

3. If the next number is exactly 5, round up only if the number to be rounded is ODD.

Ex: 1.15 and 1.25 both round to 1.2

For example, add: 28.0 cm + 23.542 cm + 25.64 cmFor example, add: 28.0 cm + 23.542 cm + 25.64 cm

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Math with significant figures:

Multiplication/division: the answer is rounded so that it has the same number of sigfigs as the value with the least number of sigfigs.

(3.205 cm)(3.65 cm)(2.05 cm) = (23.814 cm3)

#sigfigs 4 3 3 23.8 cm3

What is the answer using the correct number of sigfigs to:

(2.005 g/mL)(2.05 mL + 1.6 mL)=

(2.005 g/mL)(3.65 mL)

The six is underlined because it is the last significant digit.

Do not round off any values until the final answer!!

= 7.32 g

2 sf’s

7.3 g

2 sf’s

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A 20.0000 g weight is weighed on four different balances, and the four masses shown below were obtained. Calculate the percent error for each measurement.

19.9 g 20.04 g 20.044 g 19.9351 g

error 0.1 g 0.04 g 0.044 g 0.0649 g

Accuracy of a measurement can be determined by calculating the percent error (error = true – experimental).

% error 0.5% 0.2% 0.22% 0.324%

Percent error =error

true valuex 100

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