1 • Accuracy is how close to the true value a given measurement is. • Precision is how well a number of independent measurements agree with one another. Accuracy, Precision, and Significant Figures in Measurement
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1
• Accuracy is how close
to the true value a
given measurement is.
• Precision is how well a
number of independent
measurements agree
with one another.
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
2
• Significant Figures are the total number of digits in the measurement.
• The results of calculations are only as reliable as the least precise measurement.
• Rules exist to govern the use of significant figures after the measurements have been made.
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
3
Mass of a Tennis Ball
4
• Rules for Significant Figures:
Zeros in the middle of a number are significant
Zeros at the beginning of a number are not significant
Zeros at the end of a number and following a period are
significant
Zeros at the end of a number and before a period may or
may not be significant.
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
5
• Rules for Rounding Numbers:
If the first digit removed is less than 5 - round down
If the first digit removed is greater than 5 - round up
If the first digit removed is 5 and following numbers
are nonzero - round up
If the first digit removed is 5 and following numbers
are zero - round down
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
6
• How many significant figures does each of the
following measurements have?
(a) 0.036653 m (b) 7.2100 x 10–3 g
(c) 72,100 km (d) $25.03
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
7
• How many significant figures does each of the
following measurements have?
(a) 0.036653 m (5) (b) 7.2100 x 10–3 g (5)
(c) 72,100 km (3 or 4 or 5)(d) $25.03 (exact)
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
8
• Round off each of the following measurements.
(a) 3.774499 L to four significant figures
(b) 255.0974 K to three significant figures
(c) 55.265 kg to four significant figures
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
9
• Round off each of the following measurements.
(a) 3.774 L
(b) 255 K
(c) 55.26 kg
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
10
• Rules for Calculating Numbers:
During multiplication or division, the answer can’t
have more sig figs than any of the original numbers.
During addition or subtraction, the answer can’t have
more digits to the right of the decimal point than any
of the original numbers.
Accuracy, Precision, and Significant Figures in Measurement
Accuracy, Precision, and Significant Figures in Measurement
11
Significant Figures in CalculationsSignificant Figures in Calculations
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Significant Figures in CalculationsSignificant Figures in Calculations
13
Significant Figure CalculationsSignificant Figure Calculations
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