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Examples: 0.004500, 1200., 1.230e-4, or 1.230 × 10^-4.
A decimal marker or scientific coefficient already makes trailing precision explicit.
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This changes presentation only; counted digits and numeric error stay the same.
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Writing 12.30 g instead of 12.3 g makes a claim about precision. The extra zero does not change the quantity, but it says the measurement was recorded to a finer decimal place. Significant figures are the digits that carry that precision signal.

This convention helps prevent a calculated answer from looking more certain than its measurements. It appears in laboratory work, engineering reports, unit conversions, and science classes. Significant figures do not measure accuracy, however. A precisely written reading can still be wrong because of calibration, sampling, or method error.

Leading zeros
Zeros before the first nonzero digit locate the decimal point and do not count.
Captive zeros
Zeros between significant digits count.
Trailing zeros
Zeros at the end count when the written form makes their precision explicit.

Plain whole numbers create the main ambiguity. The final two zeros in 1200 might be measured digits or placeholders. A decimal marker such as 1200. or scientific notation such as 1.200 × 10³ communicates the intended four significant figures more clearly.

Written valueCountReason
0.0045004The leading zeros set scale; 4, 5, 0, and 0 state precision.
10024Both zeros lie between nonzero digits.
1200AmbiguousThe written form does not settle whether the trailing zeros were measured.
1.200 × 10³4The coefficient states precision; the exponent changes scale only.

Rounding should happen after the desired precision is chosen, and preferably only once at the end of a calculation. Repeatedly rounding intermediate values can accumulate error. Exact counts and defined conversion factors are also different from measured values and are not limited by the same significant-figure rule.

How to Use This Tool:

Enter the number exactly as it was written, because decimal points and trailing zeros are part of the precision evidence.

  1. Enter one decimal or scientific-notation value in Written number. Units and explanatory words do not belong in the field.
  2. Choose how Whole-number trailing zeros should be treated when a plain integer ends in zero. Keep the conventional setting unless you know those zeros were intentionally measured.
  3. Set Round to from 1 to 15 significant figures. The summary and figure audit update with the rounded value and its error.
  4. Use Rounded notation when the displayed form matters. This changes presentation, not the digit count or numeric error.

Interpreting Results:

The significant-figure count follows the selected trailing-zero convention. When the result flags ambiguity, the written integer alone cannot prove the original measurement precision; check the source record or rewrite the value in scientific notation.

Use the Digit ledger to audit a surprising count. The rounded value preserves the requested number of digits, while absolute and relative error describe the numerical change. More displayed digits do not automatically mean the source measurement became more precise.

Technical Details:

Counting starts at the first nonzero coefficient digit. Every later nonzero digit and every zero between significant digits counts. Trailing coefficient zeros count when a decimal point, exponent form, or the selected measured-zero convention makes them explicit.

Rule Core:

Digit positionCounted?Rule
Before the first nonzero digitNoLeading zero; it locates the decimal point.
Nonzero coefficient digitYesEvery nonzero coefficient digit is significant.
Zero between significant digitsYesCaptive zeros are part of the stated precision.
Trailing zero with decimal or exponent notationYesThe written coefficient preserves the zero explicitly.
Trailing zero in a plain integerConditionalIt is a placeholder unless the measured-zero convention is selected.
ExponentNoIt moves place value without changing coefficient precision.

Rounding uses decimal half-up at the first discarded coefficient digit. A discarded digit of 5 or more increments the last retained digit; a carry can increase the leading power of ten. Automatic notation switches to scientific form when an ordinary whole-number display would hide the requested precision or become unwieldy.

Formula Core:

Absolute error measures the change in the original units. Relative error expresses that change as a percentage of the original magnitude.

Ea=|r−x| Er=|r−x||x|×100%

Here, x is the parsed numeric value and r is its rounded numeric value. Calculations retain full numeric precision; displayed error values may be formatted for readability. Inputs accept signed decimals and exponent forms with exponents from −300 through 300, up to 64 coefficient digits. A zero-only token is rejected because it does not state a usable precision count.

Boundary Example:

For 1.250 rounded to two significant figures, the first discarded digit is 5. Decimal half-up rounding produces 1.3. The absolute error is 0.05 and the relative error is 4%.

References: