Case 1
- Number
- 1234.56
- Significant figures
- 3
1,230.000000
Open with these valuesSignificant Figures Calculator
1,230.000000
Result: 1,230.000000Counting starts at the first digit that is not zero, so 0.0042 has two significant figures, not five. Keep the ones you want, then look at the next digit: 5 or more rounds up. 1234.56 to three figures is 1230.
The numbers at a glance
Held fixed: Number 1,234.560000.
| Significant figures | Result |
|---|---|
| 1 | 1,000.000000 |
| 2 | 1,200.000000 |
| 3Your value | 1,230.000000 |
| 4 | 1,235.000000 |
| 5 | 1,234.600000 |
| 6 | 1,234.560000 |
Worked examples
Case 2
- Number
- 0.0042
- Significant figures
- 1
0.004000
Open with these valuesCase 3
- Number
- 98765
- Significant figures
- 2
99,000.000000
Open with these valuesHow it's calculated
round the number at its nth significant digit
- StepEnter the number you want to round.
- StepEnter how many significant figures to keep.
- StepCounting starts at the first digit that is not zero.
- ResultThe next digit decides: 5 or more rounds up.
Reference table
| Number, figures | What happens | Rounded |
|---|---|---|
| 1234.56, 3 | the next digit is a 4, so it rounds down | 1230 |
| 0.0042, 1 | leading zeros are not counted | 0.004 |
| 3.14159, 4 | π kept to four figures | 3.142 |
| 98765, 2 | the next digit is a 7, so it rounds up | 99000 |
| -0.0678, 2 | the sign is left alone | -0.068 |
| 9.99, 1 | the carry crosses into the tens | 10 |
| 1000, 2 | already at two figures | 1000 |
| 2.5, 2 | already at two figures | 2.5 |
Questions
How do I round a number to significant figures?
Count from the first digit that is not zero, find the last one you want to keep, then look at the next digit: round up if it is 5 or more, leave it if it is less. 1234.56 to three significant figures is 1230, because the fourth figure is a 4.
What are significant figures?
They are the digits that carry a number's precision, starting at the first digit that is not zero. They say how trustworthy a measurement is — a length written as 2.50 m claims more precision than one written as 2.5 m, even though the values are equal.
Do zeros count as significant figures?
It depends where they sit: leading zeros in 0.0042 never count, zeros between digits in 1002 always do, and trailing zeros after a decimal point in 2.50 do. Trailing zeros in a whole number such as 1200 are ambiguous, which is why scientific notation is often used instead.
How are significant figures different from decimal places?
Decimal places count digits after the point only; significant figures count meaningful digits from the first non-zero one, wherever the point sits. 0.0042 has four decimal places but two significant figures.
Why round to significant figures at all?
It stops you from claiming more precision than the data supports. When measurements are multiplied or divided, the result should keep only as many significant figures as the least precise input, otherwise the extra digits are noise dressed up as accuracy.
Sources and last check
Information, not professional advice.