3.3Rounding to Significant Figures
- Find the first non-zero digit. Count the required number of significant figures from there.
- Examine the next digit on the right.
- If it is 5 or more, round up. If it is less than 5, round down.
- For whole numbers, replace remaining digits with zeros as placeholders.
- For decimals, drop the remaining digits (but keep trailing zeros within the required s.f.).
Rounding a whole number to s.f.
Round to 3 significant figures.
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First 3 s.f.: digits . Next digit: ().
Round up: becomes , then add placeholder zeros.
(to 3 s.f.).
Rounding a decimal to s.f.
Round to 2 significant figures.
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Leading zeros () are not significant (Rule 3).
First 2 s.f.: digits . Next digit: (less than 5).
Round down: (to 2 s.f.).
Now you try
Round off to 2 significant figures.
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The first 2 significant figures are 4, 3. The next digit is 6 (), so round up: (to 2 s.f.).
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Now you try
Round off to 4 significant figures.
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Leading zeros are not significant. The first 4 significant figures are 2, 3, 7, 8. The next digit is 6 (), so round up: (to 4 s.f.).
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Predict
A number rounded to 2 significant figures gives . What is the largest whole number it could have been? Commit to an answer before reading on.
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Rounding to 2 s.f. here means rounding at the hundreds place.
The smallest value that rounds to is , because rounds up.
The largest whole number is , because itself rounds up to .
So the original number is anything from up to, but not including, . The answer is not : a value like still rounds to .