Number · Rounding & bounds
Chapter 1 · 4
The idea
Upper and lower bounds
Why a rounded value hides half a unit of uncertainty each way, why the upper bound is a strict "less than", how truncation differs, and how to pick the right bounds when calculating — the ÷ and − traps included.
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Number · Rounding & bounds
Upper and lower bounds
Why a rounded value hides half a unit of uncertainty each way, why the upper bound is a strict "less than", how truncation differs, and how to pick the right bounds when calculating — the ÷ and − traps included.
Why it works
Half the rounding unit each way
A measurement of "45 cm to the nearest cm" doesn't mean 45.000… — it means the true length landed somewhere that rounds to 45. Everything from up to (but not including) does that, so the error interval is— half the rounding unit each way. Nearest 10 ⇒ ; nearest 0.1 ⇒ . The unit being halved is the rounding step, not 1.
Why the top is strict
itself rounds up to 46, so it isn't in the interval — but everything below it is, no matter how close. That's why the upper bound is stated as with a strict inequality: there's no "last number before 45.5" (44.9, 45.49, 45.499… never finish). Writing the UB as 45.49 or "45.4 recurring" is the classic mark-loser: use the clean half-unit value and let the carry the meaning.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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