Count significant figures and round any number to the precision you need
| Rule | Example | Sig Figs |
|---|---|---|
| Nonzero digits always count | 4578 | 4 |
| Leading zeros never count | 0.004578 | 4 |
| Zeros between nonzero digits count | 3.005 | 4 |
| Trailing zeros after a decimal count | 2.000 | 4 |
| Trailing zeros after a decimal count | 0.050 | 2 |
| Zeros after a decimal in a mixed number count | 2500.0 | 5 |
| Trailing zeros with no decimal are ambiguous (placeholders) | 100 | 1 |
| A decimal point makes trailing zeros significant | 100. | 3 |
| Scientific notation: count only the coefficient | 6.02 × 10²³ | 3 |
| Original | Round to | Result | Note |
|---|---|---|---|
| 0.004578 | 2 sf | 0.0046 | The 7 rounds the 5 up to 6 |
| 0.004578 | 3 sf | 0.00458 | One more digit survives |
| 4578 | 2 sf | 4600 | 4.6 × 10³; zeros are placeholders |
| 123.456 | 4 sf | 123.5 | Standard half-up rounding |
| 3.14159 | 3 sf | 3.14 | π trimmed for homework |
| 99.98 | 3 sf | 100 | The carry swallows the decimal point |
| 6.022 × 10²³ | 4 sf | 6.022 × 10²³ | Already exact to 4 |
Significant figures are the digits in a number that carry real measurement information. A lab balance that reads 2.000 g is claiming precision down to the milligram; "about 2 grams" written as 2 g claims none. Science teachers grade sig figs hard because calculations should never look more precise than the measurements going in.
Three rules settle almost every case. Nonzero digits always count. Zeros sandwiched between nonzero digits count. Zeros at the edges are the tricky ones: leading zeros (0.004578) only position the decimal and never count, while trailing zeros count exactly when a decimal point is present somewhere in the number. That last asymmetry is why 100, 100., and 1.00 × 10² all describe the same magnitude with three different claims of precision.
Keep the first N significant digits, then round the Nth digit using digit N+1 (halves round away from zero, the convention most science classes use). Everything after the kept digits becomes a placeholder zero, or an exponent if you prefer scientific notation. The calculator shows both forms side by side, because 4600 written out and 4.6 × 10³ make different claims about precision on paper even though this tool treats them the same.
Type any number, including scientific notation like 6.02e23 or 1.602e-19, and pick how many sig figs to keep. The result box shows the rounded value plus the sig-fig count of what you typed, which is half the homework battle: rounding to 4 sig figs means little if you miscount the input as 4 when it was 3.
First, 0.004578 to 2 sig figs. The significant digits are 4, 5, 7, 8 (leading zeros skipped). Keep 4 and 5, then round using the 7: the 5 rounds up, giving 0.0046. Second, 4578 to 2 sig figs. Keep 4 and 5, round using the 7, and the 5 becomes 6: 4.6 × 10³, or 4600 as a plain number. Same four significant digits, same rounding step, wildly different-looking answers.
Sig figs also follow your arithmetic. Multiply or divide, and the answer keeps the least number of sig figs among the inputs: 4.56 × 1.4 = 6.384, reported as 6.4 because 1.4 has 2 sig figs. Add or subtract, and the answer keeps the least number of decimal places: 12.11 + 0.3 = 12.41, reported as 12.4 because 0.3 stops at the tenths place.
One, as written. Without a decimal point, trailing zeros in a whole number are placeholders and don't count. Write 1000. (with the decimal point shown) and it has 4 significant figures; 1.0 × 10³ has 2. If a problem says a value is known to the nearest unit, you can treat all the zeros as significant, but the number alone doesn't tell you that.
Never. In 0.004578, the three zeros after the decimal point only set the magnitude; the 4, 5, 7, and 8 are the 4 significant figures. Zeros between nonzero digits are different: 3.005 has 4 sig figs because the zeros are trapped between the 3 and the 5.
Yes. Once a decimal point is present, trailing zeros are measured digits, not placeholders: 2.000 has 4 sig figs and 0.050 has 2 (the 5 and the final 0). A chemist who writes 25.20 mL instead of 25.2 mL is telling you the measurement is precise to the hundredths place.
It aims for the half-away-from-zero convention most science classes use, so 1.35 to 2 sig figs rounds up to 1.4. But binary floating point nudges numbers that look like exact decimal halves: 3.15 to 2 sig figs comes out 3.1 and 2.675 to 3 sig figs comes out 2.67, because the stored values sit a hair under the decimal half. A few fields use banker's rounding (to the nearest even digit) instead, which this tool does not use.
Different rules. For multiplication and division, the result keeps the smallest number of sig figs among the inputs: 4.56 × 1.4 = 6.384, which rounds to 6.4 because 1.4 has 2 sig figs. For addition and subtraction, the result keeps the smallest number of decimal places: 12.11 + 0.3 = 12.41, which becomes 12.4 because 0.3 has one decimal place.
Count only the digits in the coefficient. 6.02 × 10²³ has 3 sig figs, and 2.0 × 10³ has 2. The exponent exists to handle magnitude, so it never contributes digits. That's the whole reason scientists write big and small numbers this way: it removes the trailing-zero ambiguity of 1000-style notation.