Question

Consider two measurements A and B with corresponding errors a and b:

A ± a

B ± b

The following is true:

a > b and a/A < b/B

Which of the following is also true:

Group of answer choices

"b" is a larger error than "a", "a" is a less significant error than "b"

"a" is a larger error than "b", "b" is a less significant error than "a"

"a" is a larger error than "b", "a" is a less significant error than "b"

"b" is a larger error than "a", "b" is a less significant error than "a"

Answer 1

Answer 2

Since a > b and a/A < b/B, we can conclude that "a" is a larger error than "b" and "a" is a less significant error than "b". This means that option (C) is correct: "a" is a larger error than "b", and "a" is a less significant error than "b".

To understand why this is the case, we can consider the relative sizes of a and b with respect to A and B. The fact that a/A < b/B means that the ratio of a to A is smaller than the ratio of b to B. This implies that the error a is a smaller fraction of the measured value A than the error b is of the measured value B.

For example, suppose A = 100 and B = 50, and suppose a = 2 and b = 5. Then a/A = 0.02 and b/B = 0.1, so a/A < b/B. This means that the error a = 2 is smaller relative to the measured value A = 100 than the error b = 5 is relative to the measured value B = 50. In other words, the error a is a less significant error than the error b. However, since a > b, we know that a is a larger error than b.