1.005 to two decimal places
1.01 or 1.00
Ties away from zero gives 1.01. Ties to even gives 1.00, because its last retained digit is even. The entered decimal is treated exactly.
Numbers
Rounding Calculator
Choose the precision and the rounding rule. Compare how five methods handle the same number.
Round a number
Rounded number
Enter a number, then select Round.
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Calculations stay in your browser. Successful results appear in your tab's recent calculations.
Rounding examples
−2.7 to an integer
Floor −3 · Truncate −2
Floor moves downward on the number line. Truncation removes the fractional part. Ceiling also gives −2 in this example.
12,345 to three figures
1.23 × 10^4
The decimal value is 12,300. Scientific notation makes the three retained figures clear; plain integer notation can leave trailing zeros ambiguous.
How the precision works
Rounding to p decimal places selects a multiple of 10−p. Zero places means an integer; −1 means a multiple of ten; −2 means a multiple of one hundred. This tool accepts −20 through 20 places.
For a nonzero value with first nonzero digit at 10e, rounding to s significant figures uses a rounding increment of 10e−s+1. Choose 1 through 20 figures. A carry can change the exponent: 9.99 to two figures becomes 1.0 × 10^1.
Trailing zeros preserve your requested output precision. Adding zeros does not make a measurement more accurate. For zero, this tool uses exponent 0 and the requested mantissa length, for example 0.00 × 10^0 for three figures; it does not infer measurement precision from the input.
Inputs may have a leading + or keyboard minus (-), with up to 100 digits before and 100 after the decimal point, including leading and trailing zeros. The total input limit is 220 characters. Enter 0.5 rather than .5. Expressions, thousands separators, and scientific input notation are not accepted.
Rounding uses exact integer arithmetic on the entered decimal digits, including the midpoint comparison. The rounded number is the exact output of the selected rule. The note tells you whether its numeric value differs from the input. Negative zero is displayed as zero.
Rule references: ECMA-402 rounding modes and OpenStax — significant figures. The default ties-away rule corresponds to ECMA-402's halfExpand. See the calculation policy for other tools' display rules.
Common questions
Why can two calculators round 1.005 differently?
They may use different tie rules or store the input as a nearby binary floating-point value. This tool reads the typed decimal exactly and applies your chosen rule. Ties away from zero gives 1.01 at two decimal places.
Does “round down” mean floor or truncate?
The phrase is ambiguous for negatives. Floor sends −2.7 to −3; truncation sends it to −2. Choose the named direction here instead of relying on “up” or “down.”
Should I round after every step?
For ordinary numerical calculations, keep intermediate precision and round the final result. A specific process, such as a payment schedule, may require rounding at each step; follow that process's rules.
Can this determine the significant figures of my measurement?
No. You select the target number of figures. Measurement uncertainty, units, and the way the value was measured determine appropriate precision; the calculator does not infer those.