Physics and chemistry answers must be reported to the right number of significant figures. Enter a value and the number of significant figures or decimal places you need to get the correctly rounded result and its scientific notation.
Enter the number.
Choose significant figures or decimal places and how many.
Read the rounded value.
Rule: Count from the first non-zero digit, then round the last kept digit
The significant figures calculator rounds a number either to a chosen number of significant figures, the digits that carry real information about precision, or to a chosen number of decimal places. It also shows the rounded value in scientific notation, the form used in physics and chemistry lab reports.
In Class 11 physics and chemistry, answers are expected to have the right number of significant figures, because a result cannot be more precise than the measurements behind it. If a length is measured with a ruler to 0.1 cm, quoting an area to eight decimal places is misleading. Engineers, lab technicians and data analysts round for the same reason. The calculator handles the fiddly cases, such as leading zeros in 0.004567, which are not significant, and rounding that carries over into a new digit.
1. Find the first non-zero digit, reading from the left. Counting of significant figures starts there; leading zeros never count.
2. Count the number of significant figures you want to keep, n.
3. Look at the next digit after the n-th significant figure.
4. If that digit is 5 or more, increase the last kept digit by 1; if it is less than 5, leave it unchanged.
5. Drop the remaining digits. Before the decimal point replace them with zeros to keep the place value, for example 48,760 to 3 s.f. is 48,800.
6. For decimal places, count digits after the decimal point instead of from the first non-zero digit.
7. Write the result in scientific notation, a × 10^k, to make the number of significant figures unambiguous.
All non-zero digits are significant. Zeros between non-zero digits, as in 2.05, are significant. Leading zeros, as in 0.0032, only show the decimal position and are not significant, so 0.0032 has two. Trailing zeros after a decimal point, as in 2.50, are significant because someone chose to write them. Trailing zeros in a whole number such as 1500 are ambiguous: they might be measured or just placeholders. Scientific notation removes the doubt, since 1.50 × 10³ clearly has three.
Significant figures measure relative precision, while decimal places measure absolute precision. Rounding 0.004567 to 2 decimal places gives 0.00, which throws away everything, but rounding it to 2 significant figures gives 0.0046. Rounding 45,678.9 to 2 significant figures gives 46,000, but to 2 decimal places it stays 45,678.90. Use significant figures for scientific measurements that vary in size, and decimal places for money and quantities with a fixed unit such as paise.
When multiplying or dividing, give the answer to the fewest significant figures among the inputs. When adding or subtracting, give it to the fewest decimal places among the inputs. Round only at the end, keeping extra digits in between. One display note: the rounded value field shows a plain number, so a result such as 2.50 appears as 2.5, dropping a significant trailing zero. The scientific notation field keeps it, so use that when the trailing zero matters.
Harsh timed a simple pendulum in the physics lab and his calculator shows a period of 1.98347 s, but his stopwatch readings justify only 3 significant figures.
Keep 3 significant figure(s), counting from the first non-zero digit: 1.98347 → 1.98
Scientific notation: 1.98 × 10^0
Answer: Rounded value 1.98; Scientific notation 1.98 × 10^0
Counting leading zeros, such as saying 0.0045 has four significant figures instead of two.
Rounding in several stages, such as 2.3449 to 2.345 and then to 2.35, instead of rounding once to 2.34.
Dropping digits before the decimal point without replacing them with zeros, turning 48,760 into 488.
Mixing up significant figures with decimal places when a question asks for one of them.
Rounding intermediate results in a multi-step calculation, which builds up error.
Reporting physics and chemistry lab results to the correct precision.
Rounding answers in Class 11 and 12 numericals as board exams expect.
Presenting engineering measurements and tolerances clearly.
Rounding money to 2 decimal places, or large figures to a few significant digits for reports.
Writing very large or small quantities in scientific notation.
Are leading zeros significant?
No. In 0.0045 only 4 and 5 are significant.
How many significant figures should my answer have?
In multiplication and division, use the fewest significant figures among the measured values.