Problem 1.1 The value of is 3.14159265. . . If C is the circumference of a circle and r is its radius, determine the value of r/C to four signi?cant digits.
Solution: C D 2 r )
r 1 D D 0.159154943. C 2 r D 0.1592 C
To four signi?cant digits we have
Problem 1.2 The base of natural logarithms is e D 2.718281828 . . . (a) (b) (c) Express e to ?ve signi?cant digits. Determine the value of e2 to ?ve signi?cant digits. Use the value of e you obtained in part (a) to determine the value of e2 to ?ve signi?cant digits.
Solution: The value of e is: e D 2.718281828
(a) (b) (c) To ?ve signi?cant ?gures e D 2.7183 e2 to ?ve signi?cant ?gures is e2 D 7.3891 Using the value from part (a) we ?nd e2 D 7.3892 which is not correct in the ?fth digit.
[Part (c) demonstrates the hazard of using rounded-off values in calculations.]
Problem 1.3 A machinist drills a circular hole in a panel with a nominal radius r D 5 mm. The actual radius of the hole is in the range r D 5 ? 0.01 mm. (a)