How to round a number to significant figures

For 0.004826, the first significant digit is 4. The zeros before it locate the decimal point; they do not count towards the requested number of significant figures. To keep three significant figures, retain 4, 8 and 2, then inspect the next digit, 6.

Use the usual school rounding convention: if the first discarded digit is 5 or greater, increase the last retained digit by one; if it is less than 5, leave that digit unchanged. Thus 0.004826 becomes 0.00483 to three significant figures. If a question explicitly specifies another tie-breaking convention, follow it.

To round 73842 to two significant figures, keep the 7 and 3. The next digit is 8, so the 3 increases to 4. Replace the remaining integer places with zeros: the answer is 74000, not 74.

Scientific notation makes the intended precision clear: 7.4 × 10⁴ has two significant figures. Writing 74000 alone can leave the significance of its trailing zeros ambiguous unless the question states the precision.

For a check, compare the sizes of the original and rounded values. Changing 73842 into 74 changes its scale by about a thousand, which is far beyond rounding.

Zeros between nonzero digits count. The number 3.007 has four significant figures. Trailing zeros after a decimal point also express precision: 2.50 has three significant figures, while 2.5 has two. These are the same numerical value written with different stated precision.

For 0.02040, the significant digits are 2, 0, 4 and the final 0. The zeros before the 2 do not count. To three significant figures, write 0.0204. To two significant figures, write 0.020, preserving the final zero because it is the second significant digit.

If you round 6.997 to three significant figures, carrying changes the retained digits and the answer is 7.00. Writing only 7 would no longer communicate three significant figures.

Decimal places count digits after the decimal point, including zeros before the first nonzero digit. Significant figures count from the first nonzero digit instead. For 0.004826, three decimal places gives 0.005, while three significant figures gives 0.00483.

For 482.6, two decimal places gives 482.60, while two significant figures gives 480, or more clearly 4.8 × 10². Copy the requested form and precision beside your working before rounding.

Adding a zero to show a requested decimal format does not create a more accurate measurement. Keep a distinction between formatting a number and claiming additional measurement precision.

Keep calculator digits or an exact fraction during intermediate steps, then round the final result as requested. Repeated rounding can push an answer across a boundary.

For example, 1.249 rounded directly to two significant figures is 1.2 because the third significant digit is 4. Rounding it first to three significant figures gives 1.25; rounding that result to two gives 1.3 under the usual convention. The intermediate rounding changed the answer.

If you write an intermediate result, keep enough extra digits and use your calculator’s stored value for the next operation. Do not assume that every question wants the same number of significant figures: use the stated instruction or the precision convention required for that task.

Use this record: original value; requested significant figures; first nonzero digit; last retained digit; first discarded digit; rounded value with place value preserved; number of significant figures in the written answer.

Try rounding 0.009964 to three significant figures. Keep 9, 9 and 6. The next digit is 4, so the answer is 0.00996. Now round the same original to two significant figures: keep 9 and 9, inspect 6, and carry to obtain 0.010. The 1 and final 0 express the two significant figures.

As a final size check, the two-significant-figure answer 0.010 is close to 0.009964. An answer of 0.10 would be ten times too large, suggesting that a decimal position moved during the carry.