Modern Engineering Thermodynamics

18 CHAPTER 1: The Beginning
A number reported as 0.000452 has only three significant figures (4, 5, and 2), since the leading zeros are used
simply to fix the decimal point. But the number 7305 has four significant figures. The number 2300 may have
two, three, or four significant figures. To convey which ending zeros of a number are significant, it should be
written as 2.3 × 10 3 if it has only two significant figures, 2.30 × 10 3 if it has three, and 2.300 × 10 3 if it has four.
Remember that the identification of the number of significant figures associated with a measurement comes
only through a detailed knowledge of how the measurement is carried out.
Computations often deal with numbers having unequal numbers of significant figures. A number of rules have been
developed for various computations. The rule for addition and subtraction of figures follows. Next comes the rule
for multiplication and division of figures. The operation of rounding values up or down also follows specific rules.
Do you need to maintain the correct number of significant figures in all the steps of a calculation? No, just keep
one or two more digits in intermediate results than you need in your final answer. These rules are summarized
in Table 1.6.
RULE FOR ADDITION AND SUBTRACTION
The sum or difference of two numbers should contain no more significant figures farther to the right of the decimal point than
occur in the least accurate number used in the operation. For example, 114.2 + 1.31 = 115.51, which must be rounded to
115.5, since the least precise number in this operation is 114.2 (having only one place to the right of the decimal point).
Similarly, 114.2 – 1.31 = 112.89, which must now be rounded to 112.9.
This rule is vitally important when subtracting two numbers of similar magnitudes, since their difference may be much less
significant than the two numbers that were subtracted. For example, 114.212 − 114.0 = 0.212, which must be rounded to
0.2 since 114.0 has only one significant figure to the right of the decimal point. In this case, the result has only one significant
figure even though the “measured” numbers each had four or more significant figures.
RULE FOR MULTIPLICATION AND DIVISION
The product or quotient should contain no more significant figures than are contained in the term with the least number of significant
figures used in the operation. For example, 114.2 × 1.31 = 149.602, which must be rounded to 150, since the term
1.31 contains only three significant figures. Also, 114.2/1.31 = 87.1756, which must be rounded to 87.2 for the same reason.
RULES FOR ROUNDING
1. When the discarded value is less than 5, the next remaining value should not be changed. For example, if we round
114.2 to three significant figures it becomes 114; if we rounded it to two significant figures it becomes 110; and
rounding it to one significant figure produces 100.
2. When the discarded value is greater than 5 (or is 5 followed by at least one digit other than 0), the next remaining
value should be increased by 1. For example, 117.879 rounded to five significant figures is 117.88; rounded to four
significant figures, it becomes 117.9; and rounding it to three significant figures produces 118.
3. When the discarded value is exactly equal to 5 followed only by zeros, then the next remaining value should be rounded
up if it is an odd number, but remain unchanged if it is an even number. For example, 1.55 rounds to two significant
figures as 1.6, and 1.65 also rounds to two significant figures as 1.6.
Table 1.6 Significant Figures
Written Form of a Number
Number of Significant Figures Represented
by These Numbers
3 or 0.1 or 0.01 or 0.001 or 3 × 10 –5 or 5 × 10 4 One significant figure
3.1 or 50. or 0.010 or 0.00036 or 7.0 × 10 3 Two significant figures
3.14 or 500. or 0.0155 or 0.00106 or 7.51 × 10 4 Three significant figures
3.142 or 1,000. or 0.1050 or 0.0004570 or 3.540 × 10 8 Four significant figures
3.1416 or 10,000. or 0.0030078 or 1.2500 × 10 4 Five significant figures
3.14159 or 100,000. or 186,285 Six significant figures