Math 151A Homework #3 – due Wednesday 10/25, in class
Show all your work!
1. Trinary computing.
Imagine we’ve invented a trinary (base 3) computer, which stores information as trits
(trinary bits) which can take on values 0,1 or 2. If (as with binary computers) the tri-
nary computer uses 52 trits to hold the mantissa (a.k.a. the trinary fraction), how many
decimal digits of precision can we expect?
2. k-digit rounding approximation (Problem 24 of section 1.2)
Suppose that f l(y) is a k-digit rounding approximation to y. Show that
y−fl(y)
y≤0.5×10−k+1.
[Hint: If dk+1 <5, then fl(y) = 0.d1d2. . . dk×10n. If dk+1 ≥5, then fl(y) = 0.d1d2. . . dk×
10n+ 10n−k.]
3. Approximating π
Compute the absolute error and relative error for approximating πby 22/7. How many
significant digits is the approximation good to?
4. Approximating e
a. The number ecan be approximated by the sequence
e≈
n
X
k=0
1
k!.
If n= 4, what is the relative error and number of significant digits in this approximation
of e? How about when n= 8?
b. The number ecan also be approximated by
e≈n· √2πn
n!!1/n
What is the relative error and number of significant digits when n= 4, n= 8, and
n= 20?
