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3 Responses
I always have to remind myself: 0.0500 has three sig figs (5,0,0-leading zeros don’t count), and plain 100 is usually taken as 1 sig fig unless you write 100. or 1.00×10^2 to show three. For multi-step work, keep a couple of guard digits and round only at the end using the usual rules (×/÷: fewest sig figs; +/−: fewest decimal places)-nice refresher here: https://www.khanacademy.org/math/arithmetic/arith-review-rounding-significant-figures/arith-review-significant-figures/v/significant-figures; what kind of problems are making the rounding feel tricky?
Great question-zeros can be sneaky little placeholders. Think of them like chairs: some are occupied (significant) and some are just there to line things up. In 0.0500, the leading zeros just set the decimal place, so they don’t count, but the 5 and the two trailing zeros do, so that’s 3 significant figures. For 100 without a decimal point, it’s ambiguous; in most classes we treat it as 1 significant figure unless you make it clear otherwise-100. (with a decimal) or 1.00×10^2 both signal 3 significant figures. General vibe: leading zeros never count, zeros sandwiched between nonzeros do (like in 1002), and trailing zeros only count if there’s a decimal point shown. For rounding, keep full calculator precision through the steps (or at least a couple of extra “guard” digits) and round once at the end. When you finally round: for multiply/divide, match the fewest significant figures among your inputs; for add/subtract, match the fewest decimal places. That routine keeps rounding errors from piling up.
Great question-tidying the rules makes everything click. Zeros only count in certain places: leading zeros never count (they’re just placeholders), zeros between nonzero digits always count, and trailing zeros count only if a decimal point is shown. So 0.0500 has three significant figures (the 5, and the two trailing zeros after the 5). The number 100 without a decimal point is ambiguous in everyday writing, but by the usual convention it’s treated as 1 significant figure; to show 3 significant figures you’d write 100. (with a decimal point) or, even clearer, 1.00 × 10^2. A quick mental check I use: “Is there a written decimal point?” If yes, trailing zeros are significant; if no, they usually aren’t.
For rounding across steps, the safest habit is: don’t round until the end. Keep full calculator precision (or at least 2 “guard digits”) in intermediate results. Then apply the rule that matches the operation: for multiplication/division, the result should have as many significant figures as the input with the fewest; for addition/subtraction, match the least precise decimal place. Exact counts and defined conversion factors (like 60 seconds in a minute) don’t limit the sig figs. I learned this the hard way in a first-year lab: I rounded after every step in a density calculation and ended up off by a noticeable amount; my TA circled “round once at the end!” and showed me to write 100. or 1.00 × 10^2 when I really meant three significant figures. That little discipline made my results both cleaner and easier to justify.