Answer
a. This relationship is exact because 10 cm = 1 dm exactly. Every single decimeter, by definition, is equal to ten centimeters, not 10.01 nor 9.99. All the proportions that involve the metric system are in fact exact, because the prefixes always suggest the same, kilo- means a thousand times, milli- means one thousandth of, etc. Conversion factors between the metric system are not exact (expect for 1in.=2.54 cm), however.
b. This quantity is exact. You cannot have anything but a whole number of players, therefore the quantity is exact.
c. This quantity is not exact. The mass reading depends on the equipment used to measure ir. When it comes to mass, there can be any number of significant figures, to show certainty, but it is never exact.
d. This quantity is not exact. Just like mass, temperature may vary depending on the equipment used to measure it. When dealing with physical quantities, significant figures matter, because they tell us how accurate a reading that is not exact is.
Work Step by Step
a. This relationship is exact because 10 cm = 1 dm exactly. Every single decimeter, by definition, is equal to ten centimeters, not 10.01 nor 9.99. All the proportions that involve the metric system are in fact exact, because the prefixes always suggest the same, kilo- means a thousand times, milli- means one thousandth of, etc. Conversion factors between the metric system are not exact (expect for 1in.=2.54 cm), however.
b. This quantity is exact. You cannot have anything but a whole number of players, therefore the quantity is exact.
c. This quantity is not exact. The mass reading depends on the equipment used to measure ir. When it comes to mass, there can be any number of significant figures, to show certainty, but it is never exact.
d. This quantity is not exact. Just like mass, temperature may vary depending on the equipment used to measure it. When dealing with physical quantities, significant figures matter, because they tell us how accurate a reading that is not exact is.
