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Certainty, Uncertainty and Significant Figures

Scientific Measurement

• calibrations

• Certainty in measurement depends upon the calibrations and the ability of the user.

Certainty and Uncertainty


Example: Consider a centigram balance whose pointer lies between 32.5 and 32.6. A casual

user records the mass 32.5 g while a skillful user records 32.54 g.

Certainty and Uncertainty32.54 g

The 3,2 and 5 are called certain digits because the were read from the

calibrations on the scale.

The 4 is said to be uncertain because it is the estimated value between the

.5 mark and the .6 mark


RULE

In a recorded measurement, the last written digit is assumed to be

uncertain.

Significant Figures(”Sig Figs”)

Significant figures are defined as all the digits in a measurement that are certain followed by one digit which

is an estimate.

Rules for Counting Significant Figures

• All digits 1-9 inclusive are significant.

• Example: 12.9g has 3 sig figs


• Zeros between two sig figs are significant

• Example: 105ml has 3 sig figs


• Trailing zeros, after a decimal point, indicate certainty and are significant.

• Example: 7.00km has 3 sig figs


• Zeros that serve only to place the decimal point are NOT significant.

• Example: 0.001mg has 1 sig fig

700 mg has 1 sig fig

Calculating with Significant Figures

Determine the perimeter of Rectangle D length measured with ruler B 12.0 cm length measured with ruler B 12.0 cm width measured with ruler C 10.52 cm width measured with ruler C 10.52 cm

45.04 cm

Answer :


Determine the perimeter of Rectangle D length measured with ruler B 12.0 cm length measured with ruler B 12.0 cm width measured with ruler C 10.52 cm width measured with ruler C 10.52 cm

45.04 cm

Answer : 45.0 cm

Rules for Calculating with Significant Figures

When adding and subtracting, limit and round your answer to the least number of decimal places in any of

the addends, minuends or subtrahends.


Determine the Area of Rectangle D Recorded width +0.1 12.0 cm x 10.5 cm = 126.0 cm2 recorded values 12.0 cm x 10.4 cm = 124.8 cm2 Recorded width -0.1 12.0 cm x 10.3 cm =123.6 cm2

Answer :


Determine the Area of Rectangle D Recorded width +0.1 12.0 cm x 10.5 cm = 126.0 cm2 recorded values 12.0 cm x 10.4 cm = 124.8 cm2 Recorded width -0.1 12.0 cm x 10.3 cm =123.6 cm2

Answer : 125 cm3

Rules for Calculating with Significant Figures

When multiplying and dividing, limit and round your answer to the least number of significant figures of any

factor, divisor or dividend.

Precision and Accuracy

Precision is indicated by the amount of agreement between two or more

measurements that have been made in the same way.


Student A Student B17.63g 17.63g17.64g 17.60g17.62g 17.66g

17.63g mean 17.63g

Even though the averages are the same, student B has a variation of .06 while student A has a variation of .02 g indicating greater precision.


Accuracy indicates the nearness of a measurement of its “true” value and

requires an accurate instrument.

An accurate instrument is one that has been calibrated to an accepted

standard.

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