Rounding Calculator
Round numbers to the nearest whole number, decimal place, place value, or significant figure. This calculator also shows why the number rounds up or down, highlights the decision digit, and gives a clear step-by-step explanation.
Background
Rounding replaces a number with a nearby value that is easier to read, compare, or use in later calculations. The key idea is simple: look at the digit just to the right of the place you want to keep. If that digit is 5 or more, round up. If it is 4 or less, keep the kept digit the same and drop the rest.
How to use this calculator
- Enter the number you want to round.
- Choose a mode: nearest place value, decimal places, significant figures, or round up / down.
- Pick the exact target, such as nearest tenth, 2 decimal places, or 3 significant figures.
- Click Calculate to see the rounded result and explanation.
- Use the digit highlight visual to see which digit was kept and which digit made the rounding decision.
- Use Copy result if you want to paste the answer somewhere else.
How this calculator works
- Nearest place value: rounds to a named place such as ones, tens, hundreds, tenths, or hundredths.
- Decimal places: keeps a chosen number of digits after the decimal point.
- Significant figures: keeps a chosen number of meaningful digits, starting with the first nonzero digit.
- Round up / down: lets you apply ceiling, floor, or truncate behavior instead of standard nearest rounding.
- Decision digit: the digit immediately to the right of the kept place determines whether the number rounds up or stays the same.
- Trailing zeros: can be preserved when they help communicate the intended precision, such as 15.50.
Formula & Rules Used
Standard rounding rule: look at the digit immediately to the right of the kept place.
If the decision digit is 5 or more: increase the kept digit by 1, then drop the rest.
If the decision digit is 4 or less: keep the kept digit the same, then drop the rest.
Round up (ceiling): move to the smallest allowed value that is greater than or equal to the original number.
Round down (floor): move to the greatest allowed value that is less than or equal to the original number.
Truncate: cut off extra digits without standard nearest rounding.
Example Problems & Step-by-Step Solutions
Example 1 — Round to the nearest tenth
Round 15.496 to the nearest tenth.
- The tenth digit is 4.
- The digit to its right is the hundredth digit, 9.
- Because 9 ≥ 5, round the tenth digit up.
- The result is 15.5.
Example 2 — Round to 2 decimal places
Round 72.445 to 2 decimal places.
- Keep two digits after the decimal: 72.44.
- The next digit is 5.
- Because 5 ≥ 5, round the last kept digit up.
- The result is 72.45.
Example 3 — Round to 3 significant figures
Round 0.004876 to 3 significant figures.
- The first three significant digits are 4, 8, and 7.
- The next digit is 6.
- Because 6 ≥ 5, round the 7 up to 8.
- The result is 0.00488.
Frequently Asked Questions
Q: What digit decides whether a number rounds up or down?
The digit immediately to the right of the place you want to keep is the decision digit.
Q: What happens if the decision digit is 5?
In standard rounding, 5 means round up.
Q: What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point. Significant figures count meaningful digits starting with the first nonzero digit.
Q: Can this calculator round negative numbers?
Yes. It supports both positive and negative numbers.
Q: Why would I keep trailing zeros?
Trailing zeros can show the intended precision, such as writing 15.50 instead of 15.5.
Q: What is truncate?
Truncate means cut off extra digits without using standard nearest rounding.
