What Is Significant Figure Rounding?
Significant figures are the digits in a number that carry meaning. Rounding to a set number of them keeps a result no more precise than the measurements behind it.
Type the number exactly as written so trailing zeros after a decimal point are counted. Choose how many significant figures to keep and a rounding rule: nearest, always up, or truncate. The calculator returns the rounded value, the scientific notation, the sig fig count of your input and a table of the same number at 1 to 6 sig figs.
The rules are simple: leading zeros never count, zeros between digits always count, and trailing zeros count only after a decimal point. A whole number such as 1200 is ambiguous, so scientific notation is the clearest way to show its precision.
How to Use the Significant Figure Rounding Calculator
- Type the number as written.
- Choose how many significant figures to keep.
- Read the rounded value, the scientific notation and the count for your input.
Significant Figure Rounding Formula
Rounding position
Scientific notation
Significant Figure Rounding Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| k | Number of significant figures to keep | |
| x | The number you are rounding | |
| Rounding digit | The first digit after the last one kept | 5 or more rounds up |
| a × 10ⁿ | Scientific notation form | 1 ≤ |a| < 10 |
Significant Figure Rounding Worked Example
With the example values loaded in the calculator above, the steps are:
- Your number has 5 significant figures. You asked for 3.
- Keep the first 3 non-zero digits counting from the left, starting at the first non-zero digit.
- Digits from the first non-zero digit: 4567. The digit after position 3 decides the rounding (5 or more rounds up).
- Result: 0.00457.
Result: Rounded to 3 significant figures = 0.00457; Scientific notation = 4.57 × 10^-3.
Counting significant figures
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits count | 4,567 | 4 |
| Zeros between digits count | 1,005 | 4 |
| Leading zeros do not count | 0.00456 | 3 |
| Trailing zeros after a decimal point count | 4.500 | 4 |
| Trailing zeros in a whole number are ambiguous | 1,200 | 2 (or more if stated) |
Worked example: 0.0045678 to 3 sig figs
The first non-zero digit is 4, so the three significant digits are 4, 5 and 6. The next digit is 7, which is 5 or more, so the 6 rounds up to 7.
The result is 0.00457, which is 4.57 × 10^−3 in scientific notation.
Where Significant Figure Rounding Is Used
Science and lab reports
Report a result with the precision the measurement justifies.
Maths homework
Check rounding to 2, 3 or 4 significant figures.
Data tables
Present numbers consistently at a chosen precision.
Common Significant Figure Rounding Mistakes to Avoid
- Write whole numbers in scientific notation to show exactly how many digits are significant.
- Keep extra digits during a calculation and round once at the end.
Significant Figure Rounding Terms and Definitions
- Significant figures
- The digits in a number that are known with confidence, plus the first uncertain one.
Significant Figure Rounding FAQs
How do you round to significant figures?
Find the first non-zero digit, count the number of digits you want to keep, and round using the digit that follows.
Do leading zeros count as significant?
No. In 0.00456 only the 4, 5 and 6 are significant.
Do trailing zeros count?
After a decimal point, yes: 4.500 has four. In a whole number such as 1200 they are ambiguous unless you use scientific notation.
What is the difference between decimal places and significant figures?
Decimal places count digits after the point. Significant figures count meaningful digits from the first non-zero digit.
How do I show 1200 with 3 significant figures?
Write 1.20 × 10^3.
Why not round at every step?
Early rounding compounds the error. Round only the final answer.