Significant Figures
45
PROBLEM:
A student weighs a beaker on a triple-beam balance, finding values of 50.32 g,
50.31 g, and 50.31 g in successive weighings. Express the average weight to the
proper number of significant figures.
SOLUTION:
To obtain the average, add the weights and divide by 3.
50.32 g
50.31 g
50.31 g
Total = 150.94g
Average = 50.3133 g
Because the weighings disagree in the second decimal place, it is not proper to
give the weight to more than the second decimal place. The average weight, to the
proper number of significant figures, is 50.31 g.
Final Zero as Significant Figure
Final zeros after the decimal point are significant figures and are used to
indicate the decimal place to which the measurements are reliable. Thus 1.0 cm
indicates a length reliably known to tenths of a centimeter but not to hundredths
of a centimeter, whereas 1.000 cm indicates a length reliably known to thousandths of a centimeter. A very common mistake is leaving out these zeros
when the measured quantity has an integral value.
PROBLEM:
Give the value of a 10 g weight to the proper number of significant figures. The
balance on which the weight is used will respond to weight differences of 0.0001 g.
SOLUTION:
The weight is given as 10.0000 g, to show that it is reliable to 0.0001 g.
When a number has no zeros after the decimal point, final zeros before the
decimal point may or may not be significant, depending upon the usage. If we
say that there are 1000 students enrolled in a school, all the zeros probably are
significant. But if the population of a city is given as 360,000, the last two or
three zeros are not significant, because daily changes make the population
uncertain by perhaps several hundred persons. The final zeros in this case are
used only to indicate the position of the decimal point. A convenient way to
indicate reliability of a number that has final zeros before the decimal point is to
45
PROBLEM:
A student weighs a beaker on a triple-beam balance, finding values of 50.32 g,
50.31 g, and 50.31 g in successive weighings. Express the average weight to the
proper number of significant figures.
SOLUTION:
To obtain the average, add the weights and divide by 3.
50.32 g
50.31 g
50.31 g
Total = 150.94g
Average = 50.3133 g
Because the weighings disagree in the second decimal place, it is not proper to
give the weight to more than the second decimal place. The average weight, to the
proper number of significant figures, is 50.31 g.
Final Zero as Significant Figure
Final zeros after the decimal point are significant figures and are used to
indicate the decimal place to which the measurements are reliable. Thus 1.0 cm
indicates a length reliably known to tenths of a centimeter but not to hundredths
of a centimeter, whereas 1.000 cm indicates a length reliably known to thousandths of a centimeter. A very common mistake is leaving out these zeros
when the measured quantity has an integral value.
PROBLEM:
Give the value of a 10 g weight to the proper number of significant figures. The
balance on which the weight is used will respond to weight differences of 0.0001 g.
SOLUTION:
The weight is given as 10.0000 g, to show that it is reliable to 0.0001 g.
When a number has no zeros after the decimal point, final zeros before the
decimal point may or may not be significant, depending upon the usage. If we
say that there are 1000 students enrolled in a school, all the zeros probably are
significant. But if the population of a city is given as 360,000, the last two or
three zeros are not significant, because daily changes make the population
uncertain by perhaps several hundred persons. The final zeros in this case are
used only to indicate the position of the decimal point. A convenient way to
indicate reliability of a number that has final zeros before the decimal point is to