Exercise 1: Comparing Two Measurement Errors — Possible Solution
====================================================================

COMPUTING BOTH ERRORS FOR EACH CASE
------------------------------
Case A: true value = 50.0, approximation = 50.5
    absolute error = |50.5 - 50.0| = 0.5
    relative error = 0.5 / 50.0 = 0.01  (1%)

Case B: true value = 0.05, approximation = 0.055
    absolute error = |0.055 - 0.05| = 0.005
    relative error = 0.005 / 0.05 = 0.10  (10%)

WHICH IS THE MORE SERIOUS PROBLEM
------------------------------
Case B is the more serious measurement problem, even though its
absolute error (0.005) is one hundred times smaller in raw magnitude
than Case A's absolute error (0.5). The relative error tells the
real story: Case A is off by 1% of the true value, while Case B is
off by a full 10% of its true value - ten times worse in relative
terms, despite looking far smaller in absolute terms.

WHY RELATIVE ERROR IS THE RIGHT LENS HERE
------------------------------
This chapter's own worked example (the 1,000,000.0 vs. 0.0001
true-value comparison) demonstrated the same pattern: absolute error
alone doesn't distinguish between "practically perfect" and
"completely unreliable" results, because it ignores the scale of the
number being measured. Here, the same logic applies directly: a
0.5-unit error on a measurement around 50 is a much smaller
proportional mistake than a 0.005-unit error on a measurement around
0.05, even though the raw numbers seem to suggest the opposite at
first glance. Judging measurement quality by absolute error alone
would incorrectly rank Case A as "worse," when relative error shows
the true ranking is the reverse.

WHY THIS WORKS AS AN ANSWER
------------------------------
The answer computes both error measures precisely for each case
rather than estimating, correctly identifies that the smaller
absolute error case is actually the more seriously wrong one in
relative terms, and explains the conclusion using this chapter's own
established reasoning about why relative error, not absolute error,
is the meaningful measure of trustworthiness.