Mathematics CalcyZone Calculator

Rounding Calculator

Q: What is standard half-up rounding?

Half-up rounding rounds .5 and higher up to the next integer.

Q: Should I round in the middle of a calculation?

No. Keep full precision and round only the final answer to avoid accumulated errors.

Q: How do I round to the nearest 0.05?

Divide by 0.05, round to a whole number, then multiply by 0.05.

Round numbers to nearest integer, decimal place, significant figures, or nearest fraction.

Number

Decimal Places

Calculation Solution

Rounded = 100

Precision: 150 decimal places

Mathematical Formula

Rounded = Math.round(Number * 10^d) / 10^d

Overview & Explanation

Rounding replaces a numerical value with a simpler approximation with specified precision.

How It Works

Look at the digit directly to the right of the target decimal place.
If digit is 5 or greater, round up; if less than 5, round down.

Practical Applications

Formatting currency values to 2 decimal places.

Rounding rules

To round to a chosen place, look at the next digit to the right. If it is 5 or more, round up; if less, round down. 3.14159 to two decimal places is 3.14; 2.718 to one decimal place is 2.7; 1,250 to the nearest hundred is 1,300 under the standard 'round half up' rule.

Decimal places versus significant figures

Decimal places count digits after the point; significant figures count from the first non-zero digit. 0.004567 to two decimal places is 0.00, which loses all information, but to two significant figures it is 0.0046. Scientists usually use significant figures; money uses two decimal places.

Other rounding methods

Round half to even, also called banker's rounding, sends exact halves to the nearest even digit: 2.5 becomes 2 and 3.5 becomes 4. It avoids an upward bias when many values are rounded and summed, and is the default in many programming languages and spreadsheets for some functions.

Rounding up (ceiling) and down (floor) are used for practical limits: you need 4 buses for 130 passengers in 40-seat buses, even though 130 ÷ 40 = 3.25.

Computers store decimals in binary, so a value displayed as 2.675 may actually be 2.67499999…, and rounding it to two places gives 2.67. When exact decimal rounding matters, such as in accounting, use decimal arithmetic.