As a source recedes, its apparent angular shift against background stars shrinks, which is why parallax is a monotonic proxy for distance. The catch is instrumental: below a few milliarcseconds the signal sits at the noise floor, so the most distant stars carry the largest relative uncertainty. The "smaller means farther" rule is the model's direction; the actual numbers are measurements bounded by telescope resolution.
Changing only parallax changes the inverse distance index. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Only the parallax index changes
Changing the parallax index to 1/10 gives distance index 10.
p=101,d=10
A smaller parallax index means a farther source
Because 1 is still the product, the farther label cannot be copied from the previous lesson.