Avrundningberegner

Sådan bruges denne lommeregner

1. Indtast Number
2. Indtast Decimal Places
3. Klik på knappen Beregn
4. Læs resultatet vist under lommeregneren

How Rounding Works

Rounding is the process of replacing a number with a nearby simpler number while keeping its value close to the original. The most common rule is round half up (the standard taught in schools): if the digit to be dropped is exactly 5, round up. For example, 2.35 rounded to 1 decimal place is 2.4.

The general rule: look at the digit immediately to the right of your rounding position. If it's 0-4, round down (truncate). If it's 5-9, round up. Example: round 3.14159 to 2 decimal places → look at the third decimal (1) → since 1 < 5, round down → 3.14.

Different rounding modes exist for different situations. Truncation (floor) always rounds toward zero. Ceiling always rounds up. Banker's rounding (round half to even) rounds 2.5 → 2 and 3.5 → 4, reducing cumulative rounding error in financial calculations — this is the default in many programming languages and accounting systems.

Significant Figures vs. Decimal Places

There's an important distinction between decimal places and significant figures. Decimal places count digits after the decimal point (3.14159 to 2 decimal places = 3.14). Significant figures count meaningful digits from the first non-zero digit (3.14159 to 3 significant figures = 3.14; but 0.00314159 to 3 sig figs = 0.00314).

In scientific measurement, significant figures communicate the precision of a measurement. A measurement of 3.40 m has 3 sig figs and implies the measurement is precise to the nearest 0.01 m. Writing 3.4 m implies only 2 sig figs and less precision. This system prevents false precision in reported results.

When multiplying or dividing measurements, the result should have the same number of significant figures as the least precise measurement. When adding or subtracting, round to the same decimal place as the least precise number. These rules ensure your calculations reflect actual measurement uncertainty.

Rounding in Finance, Science, and Everyday Life

In finance, rounding affects every calculation. Prices are rounded to the nearest cent. Tax calculations often truncate to avoid over-collection. Cumulative rounding errors over millions of transactions can be significant — this is why financial systems use decimal arithmetic rather than floating-point (which has inherent binary rounding errors). The classic example: $0.01 rounding error × 1 billion transactions = $10 million discrepancy.

In measurement and science, rounding is about communicating appropriate precision. Physical constants like π ≈ 3.14159265 are rounded depending on the precision needed. For most engineering, 4-5 significant figures suffice. Geodetic calculations may need 10+ digits.

In everyday contexts: rounding a restaurant bill to estimate tip, rounding minutes when scheduling, or rounding nutritional values. Mental math usually involves rounding to convenient numbers — multiplying 19 × 21 ≈ 20 × 20 = 400 (actual: 399), then adjusting.