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16
CHAPTER 2 Measurement and Problem Solving
• Exact Numbers
Exact numbers have an unlimited number of significant figures. Exact
numbers originate from three sources:
• from the accurate counting of discrete objects. For example, 3 atom
means 3.00000 ... atoms.
• from defined quantities, such as the number of centimeters in 1 m. B(
cause 100 cm is denned as 1 m,
100 cm = 1 m
means
100.00000... cm = 1.0000000... m
Note that some conversion factors are defined quantities while
others are not.
• from integral numbers that are part of an equation. For example, in tli
diameter .
.
-,
.
, equation, radius =
——.——, the number 2 is exact and therefore he
an unlimited number of significant figures.
it-mining the Number of Significant Figures in,A^umber,
EXAMPLE 2.4 How many significant figures are in each of the following numbers?
(a) 0.0035
(b) 1.080
(c) 2371
(d) 2.97 X 105
(e) 1 dozen = 12
(f) 100,000
The 3 and the 5 are significant. The
leading zeros only mark the decimal
place and are not significant.
The interior zero and the trailing
zero are significant, as are the 1 and
the 8.
Solution:
(a) 0.0035
(b) 1.080
two significant figures
four significant figures
All digits are significant.
All digits in the decimal part are (c) 2371
four significant figures
significant.
(d) 2.97 X 105
three significant figures
Defined numbers have an unlimited
number of significant figures.
unlimited
significant
(e) 1 dozen = 12
This number is ambiguous. Write as 1
ambiguous
X 105 to indicate one significant figure
or as 1.00000 X 10^ to indicate six (f) 100,000
significant figures.
BBffRJTffSH'PFI Determining the Number of Significant Figures hi a Number
How many significant figures are in each of the following numbers?
(a) 58.31
(b) 0.00250
3
(c) 2.7 X 10
(d) 1 cm = 0.01 m
(e) 0.500
(f) 2100
figures