How do you determine sig figs for ~ or … numbers?

Use the digits shown as the best indicator of precision when a number has an approximate sign; if the value is written with a trailing ellipsis, treat it as uncertain and count only the clearly provided digits as significant figures, or ask for clarification.

When a number is written with a tilde or the word approximate, it means the value is not exact and the digits you see are the ones given with meaningful precision, so count those as significant figures. If a number ends with an ellipsis it shows the value continues but the extra digits are not reliable, so only count the digits before the ellipsis as significant unless additional context says otherwise. If the number is written like three point four zero tilde, you count three digits because the zero is shown and therefore significant, but if it is written like three point four tilde you count only two digits. When you are unsure, the safest choice is to ask the person who provided the data how many digits are meant to be significant or to report your own uncertainty when you use the number.

A frequent mistake is assuming that an approximate sign means you should add hidden zeros and count them as significant, which can overstate precision; the fix is to only count digits actually shown unless the source specifies otherwise. Another common error is treating trailing zeros without a decimal point as significant when they might be placeholders; the remedy is to rewrite the number with a decimal or scientific notation to make the precision explicit. A final pitfall is ignoring context such as measurement method or instrument resolution; a quick solution is to report a reasonable uncertainty or ask for the instrument resolution if precision matters.

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Handling Sig Figs for ~ and … Numbers

1. Count shown digits as significant
2. Treat tilde as limited precision
3. Ignore digits after ellipsis
4. Count trailing zeros if shown
5. Ask for clarification when unsure

Common Sig Fig Mistakes to Avoid

1. Adding hidden zeros as significant
2. Treating trailing zeros without decimal as significant
3. Ignoring measurement method or instrument resolution

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