Калкулатор за закръгляване

Закръглете числата до различни десетични знаци, като използвате различни методи за закръгляване с решения стъпка по стъпка.

For learning and homework help — verify critical calculations independently.

Прегледано от Редакционна колегия по математика на CalculatorDrive · Последна актуализация

Калкулатор

Maximum: 20

Enter a number, select decimal places and rounding method to round the number.

Краткият отговор

Rounding replaces a number with a nearby, simpler value at a chosen precision. Look at the digit just past your cutoff: 5 or higher usually rounds the last kept digit up, below 5 leaves it unchanged — though the exact rule for an exact tie (a trailing 5) varies by method. This calculator supports five rounding modes: nearest, up, down, toward zero, and away from zero.

Key takeaways

  • "Round to Nearest" here uses banker's rounding (round half to even), so 2.5 → 2 and 3.5 → 4, not always rounding .5 up.
  • Закръгляването нагоре (таван) и закръгляването надолу (под) винаги се движат съответно към положителна или отрицателна безкрайност, независимо от знака на числото.
  • "Toward zero" and "away from zero" match floor/ceiling for positive numbers but flip for negative numbers — this is where the five modes genuinely diverge.
  • Significant figures count meaningful digits starting from the first nonzero digit, which is different from counting decimal places.

Five rounding modes compared

Mode 2.5 → −2.5 →
Nearest (banker's)2−2
Up (ceiling)3−2
Down (floor)2−3
Toward zero2−2
Away from zero3−3

Десетични знаци срещу значещи цифри

Десетичните знаци отчитат цифрите след десетичната запетая, точка. Значимите цифри броят значимите цифри, започвайки от първата ненулева цифра, където и да падне. За 0,004567: закръгляването до 3 знака след десетичната запетая дава 0,005, но закръгляването до 3 значещи цифри дава 0,00457 — много по-точен резултат, тъй като значещите цифри игнорират изцяло водещите нули.

Работен пример: същият брой, пет начина

The table above shows exactly why the choice of mode matters: 2.5 and −2.5 are the same distance from zero, yet each rounding mode can send them to different results depending on the number's sign. "Round to Nearest" and "Toward zero" happen to agree here, but that won't always be the case for other numbers.

Често срещани грешки, които трябва да избягвате

  • Assuming "round to nearest" always rounds a trailing 5 up — this tool, like Python and many technical systems, rounds half to even instead.
  • Confusing "toward zero" and "away from zero" with floor and ceiling — they're identical for positive numbers but flip for negative numbers.
  • Mixing up decimal places and significant figures — a small number like 0.004567 loses most of its precision if rounded to "3 decimal places" instead of "3 significant figures."
  • Rounding at every intermediate step of a multi-step calculation instead of only at the very end, which compounds small errors.

Свързани калкулатори

Често задавани въпроси

Какво означава закръгляване на число?

Rounding replaces a value with a nearby simpler number at a chosen precision — nearest whole number, tenth, hundredth, or significant figure.

What is the standard rounding rule for 5?

Когато цифрата след вашето прекъсване е 5, последвана само от нули, много конвенции закръглят половината нагоре: 2,5 до 3, −2,5 до −3. Някои системи използват банково закръгляване (до дори).

What are significant figures?

Significant figures are the meaningful digits in a measurement. Rounding to three significant figures keeps three reliable digits: 0.004567 becomes 0.00457.

When should you round in multi-step calculations?

Keep extra digits during intermediate steps and round only the final answer. Early rounding compounds error.

How do I use this rounding calculator?

Enter a number, choose decimal places or significant figures, pick a rounding mode, and click Calculate to see the rounded result.

Why does "Round to Nearest" round 2.5 to 2, not 3?

The "Round to Nearest" mode uses banker's rounding (round-half-to-even): when a value falls exactly halfway between two targets, it rounds to whichever one is even, not always up. That is why 2.5 rounds to 2 and 3.5 rounds to 4 — both land on the nearest even number. This reduces systematic upward bias when rounding large batches of numbers, which is why it is the default in Python and many statistical tools, even though "round half up" is more commonly taught in school.

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