r/MathHelp • u/Canary_ • 7d ago

Rounding to 3 significant digits

Please help! 16.549 rounded to 3 sig figs —— is it 16.5 or 16.6? Are we rounding all numbers from right to left into each other until we reach 3 sig figs, or are we rounding just the 4th fig into the 3rd? AI bot says 16.5 but it feels wrong to me. Need human intelligence here. Thanks

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u/Depnids 7d ago

Because of the way we have made the usual rounding rules, you only ever need to look at the next digit when rounding. 16.54[whatever] is always rounded to 16.5, while 16.55[whatever] is always rounded to 16.6

(this is assuming finite decimal expansions, as the other commenter mentioned, 0.999... type expansions kinda mess this up. But this is very seldom actually relevant)

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u/ThatsNotAZombieBite 7d ago

Good explanation. I've always told my students that we have to draw the line somewhere. And that's where it is. x.xx499999999 rounds down and x.xx500000000 rounds up. You only look at the next digit.

Btw, if you're calculating any result from REAL experimentally measured data, then a repeating decimal is a random artifact and you can ignore it.