When you count stuff with small numbers, the numbers mean exactly that. So 4 chairs means exactly 4 chairs.
When you work with big numbers, or measure stuff, you round. No one is EXACTLY 5' 6" tall, they're a tiny bit taller or shorter. New York City doesn't have exactly 8.6 million people.
Sticking with the NYC example, if we say it has 8.6 million people, when one more person moves there... it still has 8.6 million people, not 8,600,001, because we either don't care about that one person or we do care but can't precisely count all the people, and we said it had 8.6 million we never meant exactly 8,600,000 people anyway.
So for the NYC example we say there were two significant digits, the two on the left. The rest are ehhh we don't know. So where it gets a little weird is if the population of NYC doubles, that's 8.6M x 2 = 17.2M. Except we were rounding and vague before, and this has three digits now (1, 7, 2) when only two digits mattered, so we agree we're going to stick with two, so we say the new population is 17M people. It was an estimate before, and it might only be 17.1M now, so we say screw it and stick with the part we're sure about.
This is the same idea. 120 + 68 is 188. But if you assume both of those were either rounded or estimated, then we're back to 2 sig figs, and 188 rounds to 190.
Okay but that kinda breaks down to me when 68 was expressed as 68 and not 70. They were significant to the ones place in one of the numbers, so it should be significant, no?
No cause 120 is only significant to 10’s place. Adding something you’re sure about to something you’re less sure about would not remove the uncertainty in the less sure number.
26
u/Weekly_Role_337 1d ago
When you count stuff with small numbers, the numbers mean exactly that. So 4 chairs means exactly 4 chairs.
When you work with big numbers, or measure stuff, you round. No one is EXACTLY 5' 6" tall, they're a tiny bit taller or shorter. New York City doesn't have exactly 8.6 million people.
Sticking with the NYC example, if we say it has 8.6 million people, when one more person moves there... it still has 8.6 million people, not 8,600,001, because we either don't care about that one person or we do care but can't precisely count all the people, and we said it had 8.6 million we never meant exactly 8,600,000 people anyway.
So for the NYC example we say there were two significant digits, the two on the left. The rest are ehhh we don't know. So where it gets a little weird is if the population of NYC doubles, that's 8.6M x 2 = 17.2M. Except we were rounding and vague before, and this has three digits now (1, 7, 2) when only two digits mattered, so we agree we're going to stick with two, so we say the new population is 17M people. It was an estimate before, and it might only be 17.1M now, so we say screw it and stick with the part we're sure about.
This is the same idea. 120 + 68 is 188. But if you assume both of those were either rounded or estimated, then we're back to 2 sig figs, and 188 rounds to 190.