Rounding Calculator

Round any number to any place value. See which digit determines the rounding with a clear visual breakdown.

Enter Number & Place Value

Rounding digit
Deciding digit

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Result

Rounded to Nearest Ones
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Original Number--
Rounded Result--
Difference--
Rounding Digit--
Deciding Digit--
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Step-by-Step Solution

How Does Rounding Work?

Rounding replaces a number with a simpler approximate value. The standard rounding rule (also called "round half up") works as follows:

  1. Identify the rounding digit -- the digit in the place you are rounding to.
  2. Look at the deciding digit -- the digit immediately to the right of the rounding digit.
  3. If the deciding digit is 5 or greater, round up (add 1 to the rounding digit).
  4. If the deciding digit is less than 5, round down (keep the rounding digit the same).
  5. Replace all digits to the right of the rounding position with zeros (for whole number places) or drop them (for decimal places).

Place Value Reference

Whole Number Places

Ones (1), Tens (10), Hundreds (100), Thousands (1,000), Ten Thousands (10,000), Hundred Thousands (100,000), Millions (1,000,000).

3,456 rounded to tens = 3,460

Decimal Places

Tenths (0.1), Hundredths (0.01), Thousandths (0.001), Ten-Thousandths (0.0001).

3.456 rounded to tenths = 3.5

Significant Figures

Rounding to a number of significant figures counts from the first non-zero digit.

0.003456 to 2 sig figs = 0.0035

Examples of Rounding

Rounding 3,456.789

  • To the nearest thousands: 3,000 (deciding digit 4 < 5, round down)
  • To the nearest hundreds: 3,500 (deciding digit 5 >= 5, round up)
  • To the nearest tens: 3,460 (deciding digit 6 >= 5, round up)
  • To the nearest ones: 3,457 (deciding digit 7 >= 5, round up)
  • To the nearest tenths: 3,456.8 (deciding digit 8 >= 5, round up)
  • To the nearest hundredths: 3,456.79 (deciding digit 9 >= 5, round up)

Why Does 5 Round Up?

The "round half up" convention means that when the deciding digit is exactly 5, we round up. This is the most commonly taught rule in schools and the most widely used in everyday life. Some scientific and financial contexts use "round half to even" (banker's rounding) to reduce bias, where 5 rounds to the nearest even number instead.

When Is Rounding Used?

  • Money: Prices are rounded to the nearest cent (hundredths).
  • Science: Measurements are rounded to significant figures matching precision.
  • Statistics: Results are rounded for readability.
  • Estimation: Quick mental math uses rounding for approximate calculations.
  • Engineering: Dimensions are rounded to manufacturing tolerances.