When will a lesser number also have a lesser absolute value?

Answer 1

When the second number is positive and has an absolute value that is bigger.

Suppose x is the first number and y the second.

Then x is smaller than y implies that

if x is non-negative then y is larger, and

if x is negative then y is less negative (nearer 0), 0 or positive

In the first case, abs(x) < abs(y), that is 0 <= x < y

In the second case, abs(x) < abs(y) if 0 < -x < y.