Precision and Accuracy

Uncertainty in Measurements

Precision and Accuracy

Uncertainty

a measurement can only be as good as the instrument or the method used to make it.

Ex. Cop’s Radar Gun vs. Car’s Speedometer.

Bank sign Thermometer vs. your skin.

Precision and Accuracy

Accepted Value A measurement deemed by scientists to be the “true measurement.”

Accuracy The Closeness or proximity of a measurement to the accepted value.

The difference between the actual measurement and the accepted value is called the ABSOLUTE ERROR.

Precision and Accuracy

Precision A proven agreement between the numerical values of a set of measurements done by the same instrument and/or method.

The Difference between the set of measurements is expressed as Absolute Deviation.

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Precision and Accuracy

Precision

refers to the reproducibility of a measurement.

Significant Figures are the digits used to represent the precision of a measurement.

SIG. FIGS. are equal to all known measurements plus one estimated digit.

Rules for Significant Digits

1) ALL NON-ZERO DIGITS ARE SIGNIFICANT

2) EXACT NUMBERS have an infinite number of significant numbers.

Exact #s are #s that are defined not measured. Numbers found by counting or used for conversions such as 100 cm = 1 m.

3) Zeros can be both significant or insignficant

Rules for Significant Digits

The Three Classes of Zeros

A. Leading Zeros Zeros that precede all of the non-zero digits are NOT significant.

Ex. 0.0025 mg

has only 2 sig. figs.( the 2 & 5)

all three zeros are not significant.

Rules for Significant Digits

B. Captive Zeros Zeros between two or more nonzero or significant digits ARE significant.

Ex. 10.08 grams

All four #s are significant

Rules for Significant Digits

C) Trailing Zeros Zeros located to the right of a nonzero or significant digit ARE Significant ONLY if there is a decimal in the measurement.

Ex. 20.00 lbs Has four sig. figs.

2000 lbs Has only 1 sig. figs

Calculations with Significant Digits

Addition and Subtraction::

The answer must be Rounded so that it contains the same # of digits to the right of the decimal point as there are in the measurement with the smallest # of digits to the right of the decimal.

13.89 years + 0.00045 years = 13.89045 years

Rounds to 13.89 years 2 places to the Rt.

Calculations with Significant Digits

Multiplication or Division

The product or quotient must be Rounded so that it contains the same # of digits as the least significant measurement in the problem.

Ex. ( 2.2880 ml )(0.305 g/ml ) = 0.69784 g

Ans. Must be rounded to 3 sig. figs.

mass = 0.698 g

Rules for Rounding Numbers

If the digit immediately to the right of the last significant figure you want to retain is ::

Greater than 5, increase the last digit by 1

Ex) 56.87 g 56.9 g

Rules for Rounding Numbers

If the digit immediately to the right of the last significant figure you want to retain is ::

Less than 5, do not change the last digit.

Ex) 12.02 L 12.0 L

Rules for Rounding Numbers

If the digit immediately to the right of the last significant figure you want to retain is ::

5, followed by nonzero digit(s) increase the last digit by 1

Ex. 3.7851 seconds 3.79 seconds

Rules for Rounding Numbers

If the digit immediately to the right of the last significant figure you want to retain is ::

5, not followed by a nonzero digit and preceded by odd digit, increase the last digit by 1.

Ex. 2.835 lbs 2.84 lbs

Rules for Rounding Numbers

If the digit immediately to the right of the last significant figure you want to retain is ::

5, not followed by a nonzero digit and preceded by even digit, do not change the last digit.

Ex. 82.65 ml 82.6 ml