Physics for Scientists & Engineers & Modern Physics, 9th Ed

Pitfall Prevention 1.4
Read Carefully Notice that the 
rule for addition and subtraction 
is different from that for multipli-
cation and division. For addition 
and subtraction, the important 
consideration is the number of 
decimal places, not the number of 
significant figures.

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Summary 
13
In this book, most of the numerical examples and end-of-chapter problems 
will yield answers having three significant figures. When carrying out estima-
tion calculations, we shall typically work with a single significant figure.
If the number of significant figures in the result of a calculation must be reduced, 
there is a general rule for rounding numbers: the last digit retained is increased by 
1 if the last digit dropped is greater than 5. (For example, 1.346 becomes 1.35.) 
If the last digit dropped is less than 5, the last digit retained remains as it is. (For 
example, 1.343 becomes 1.34.) If the last digit dropped is equal to 5, the remaining 
digit should be rounded to the nearest even number. (This rule helps avoid accu-
mulation of errors in long arithmetic processes.)
A technique for avoiding error accumulation is to delay the rounding of num-
bers in a long calculation until you have the final result. Wait until you are ready to 
copy the final answer from your calculator before rounding to the correct number 
of significant figures. In this book, we display numerical values rounded off to two 
or three significant figures. This occasionally makes some mathematical manipula-
tions look odd or incorrect. For instance, looking ahead to Example 3.5 on page 69, 
you will see the operation 217.7 km 1 34.6 km 5 17.0 km. This looks like an incor-
rect subtraction, but that is only because we have rounded the numbers 17.7 km and 
34.6 km for display. If all digits in these two intermediate numbers are retained and 
the rounding is only performed on the final number, the correct three-digit result 
of 17.0 km is obtained.
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