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Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
17
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
Rounding off numbers When you report a calculation, your
answer should have no more significant figures than the piece of
data you used in your calculation with the fewest number of significant figures. Thus, if you calculate the density of an object with a
mass of 12.33 g and a volume of 19.1 cm 3 , your answer should have
only three significant figures. However, when you divide these quantities using your calculator, it will display 0.6455497—many more
figures than you can report in your answer. You will have to round
off the number to three significant figures, or 0.646.
Here are some rules to help you round off numbers.
1. If the digit to the immediate right of the last significant figure is
less than five, do not change the last significant figure.
2. If the digit to the immediate right of the last significant figure is
greater than five, round up the last significant figure.
3. If the digit to the immediate right of the last significant figure is
equal to five and is followed by a nonzero digit, round up the
last significant figure.
4. If the digit to the immediate right of the last significant figure is
equal to five and is not followed by a nonzero digit, look at the
last significant figure. If it is an odd digit, round it up. If it is an
even digit, do not round up.
Whether you are adding, subtracting, multiplying, or dividing, you
must always report your answer so that it has the same number of
significant figures as the measurement with the fewest significant
figures.
Example Problem 2-10
Rounding Off Numbers
Round the following number to three significant figures: 3.4650.
Rule 4 applies. The digit to the immediate right of the last significant figure is a 5 followed by a zero. Because the last significant
figure is an even digit (6), do not round up. The answer is 3.46.
▲
Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
17
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
Rounding off numbers When you report a calculation, your
answer should have no more significant figures than the piece of
data you used in your calculation with the fewest number of significant figures. Thus, if you calculate the density of an object with a
mass of 12.33 g and a volume of 19.1 cm 3 , your answer should have
only three significant figures. However, when you divide these quantities using your calculator, it will display 0.6455497—many more
figures than you can report in your answer. You will have to round
off the number to three significant figures, or 0.646.
Here are some rules to help you round off numbers.
1. If the digit to the immediate right of the last significant figure is
less than five, do not change the last significant figure.
2. If the digit to the immediate right of the last significant figure is
greater than five, round up the last significant figure.
3. If the digit to the immediate right of the last significant figure is
equal to five and is followed by a nonzero digit, round up the
last significant figure.
4. If the digit to the immediate right of the last significant figure is
equal to five and is not followed by a nonzero digit, look at the
last significant figure. If it is an odd digit, round it up. If it is an
even digit, do not round up.
Whether you are adding, subtracting, multiplying, or dividing, you
must always report your answer so that it has the same number of
significant figures as the measurement with the fewest significant
figures.
Example Problem 2-10
Rounding Off Numbers
Round the following number to three significant figures: 3.4650.
Rule 4 applies. The digit to the immediate right of the last significant figure is a 5 followed by a zero. Because the last significant
figure is an even digit (6), do not round up. The answer is 3.46.
▲