Significant Figures Rounding Calculator Guide

What This Calculator Does

Count significant figures, round to a target precision, or apply precision rules to two-number arithmetic. Target rounding accepts 1–15 figures and shows both ordinary decimal form and scientific notation with trailing zeros preserved. Use the rounding calculator for a fixed number of decimal places.

When to Use It

Check significant digits in a written measurement, round to three or another number of figures, or check arithmetic precision. Measurement uncertainty and full expressions are outside the model.

Inputs Explained

Keep the original spelling: 1.200 and 1.2 have the same value but different significant counts. Use dot decimals or e scientific notation with optional signs. The mantissa allows at most 100 digits, the exponent −100 to 100 and total input 120 characters. Non-finite values and nonzero inputs that underflow to zero are rejected. Thousands separators and comma decimals are unsupported.

Target precision must be a whole number from 1 to 15. Arithmetic also needs the second number and an operator; a divisor cannot be zero. Editing clears the old result. Calculating preserves URL parameters; existing count and operation shared links still restore.

How the Calculation Works

Leading zeros do not count; interior zeros do. A written decimal point preserves trailing zeros. Plain integers without a decimal point do not count trailing zeros. Scientific mantissas count explicitly written digits: 1200 has 2, 1200. has 4, 1.200e3 has 4 and 1200e3 also counts the four explicit mantissa digits.

Target rounding parses decimal strings directly, keeps the first N significant digits and increments when the next digit is at least 5. Midpoints round away from zero. A carry updates the exponent. Scientific notation keeps exactly N figures without converting back to a number and losing zeros.

Addition/subtraction follows the least precise decimal place after exponent adjustment. In 1.20e3 + 2.3e1, the inputs are precise to tens and units respectively, so the answer rounds to tens. Multiplication/division uses the smaller significant count, capped at 15 output figures. Arithmetic uses JavaScript floating point and can inherit binary approximation.

Example

• 0.00230 has 3 significant figures; -1.200 has 4.
• 0.009995 to 3 figures gives 0.0100 and 1.00e-2.
• 999.5 to 3 figures gives 1000 and 1.00e+3.
• -1.25 to 2 figures gives -1.3 and -1.3e+0.
• 2.50 × 2.0 gives 2 figures: 5.0 and 5.0e+0.
• 1.20e3 + 2.3e1 gives 1220; decimal precision −1 means rounding to tens.

How to Understand the Result

Integer trailing zeros in ordinary notation can be ambiguous. 1000 alone does not establish three figures, while 1.00e+3 does. Significant figures and decimal places differ: 0.0100 has three significant figures and four decimal places.

Zero needs an explicit convention. This page counts one digit plus written decimal zeros: 0 has 1, 0.00 has 3. Rounding zero to N figures gives zero with N−1 decimal zeros and scientific exponent 0. This is a page convention, not an inference about measurement uncertainty.

Common Mistakes

Deleting input trailing zeros; confusing figures with decimal places; ignoring scientific form for integer results; treating the zero convention as proof of measurement precision; expecting arbitrary-precision floating-point arithmetic.

FAQ

Why do results include scientific notation?

Multiplication/division and target rounding follow significant-figure precision. Scientific notation preserves meaningful trailing zeros.

Is this the same as rounding decimal places?

Significant figures count meaningful digits across the entire magnitude; decimal places count digits after the decimal point.

How is zero handled?

For this page, zero has one digit plus its written decimal zeros: 0.00 counts as 3. Target rounding of zero to 3 figures gives 0.00 and 0.00e+0.

Notes

Use dot decimals or scientific notation, at most 100 mantissa digits and an exponent from −100 to 100. Target rounding uses decimal strings and midpoint rounding away from zero. Arithmetic uses floating point.