How many significant digits are appropriate when one or more digits are eliminated (during subtraction)?

Question

Say, for example, $50.0-49.6=0.4$. Does this result have $1$ significant figure, or $3$ (as in the data: $50.0$ and $49.6$)?

Had it been $50.0-4.6$, it is understood that the answer is $45.4$, by the rules of significant figures. How do I apply them in the "$50.0-49.6$" case?

This question deals with $50-49.6$; so a related but not the same question.

This might help: https://chemistry.stackexchange.com/a/74496/43942 — Berry Holmes, May 20 '17 at 03:43
Had checked that already. It justifies the rules-of-significant-digits[-specially-concerned-about-addition], So, doesn't answer my query; at least, I don't see it, if it does. — digikar, May 20 '17 at 04:19

score 5 · Accepted Answer · edited May 20 '17 at 05:31

There's an easy way to look at this.

Lets say the value $50.0$ refers to $\pu{50.0 cm}$ measured accurately to $\pu{0.1 cm}$, and that $49.6$ refers to $\pu{49.6 cm}$ measured accurately to $\pu{0.1 cm}$. The difference would be, as you've said, $\pu{0.4 cm}$ measured to $\pu{0.1 cm}$ accuracy.

So, yes, the answer has only one significant digit.

Your initial measurements aren't more accurate than $0.1$, so adding two extra significant digits is incorrect.

I hope this helps.

How many significant digits are appropriate when one or more digits are eliminated (during subtraction)?

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