Rounding numbers up or down is a way of approximating them to make them more manageable. In particular, decimals accurate to several places can become unwieldy and difficult to remember, so in a complex calculation, you may want to make things simpler by rounding them. When you round to the third decimal place, you're rounding to the nearest thousandth. The procedure for doing this is simple.
Locate the Third Decimal Place
Count numbers to the right of the decimal and stop when you reach the third number. That number will be the last digit in the rounded number, and your job is to decide whether to leave it as it is, which is rounding down, or add one unit, which is rounding up.
Note the Value of the Next Number
Look at the fourth number in the decimal series. Round the third number down (leave it as it is) if the fourth number is less than 5 and round up (add 1 to it) if it's more than 5. If the number is 5, you usually round up, but there's one exception in which you shouldn't. If the 5 is followed by zeros, or if it's the last number in the decimal series, you should leave the 5 untouched. The number 5 is exactly in the middle of the scale between 0 and 10, which leaves you no way to determine whether the number should be rounded up or down.
Erase All the Numbers Following the One You Rounded
After you round the third digit, remove all the numbers following the third number to express the rounded number in its streamlined form with only three digits following the decimal.
Example 1: The mathematical constant pi (π) is a nonrepeating decimal that, as far as anyone knows, has an infinite number of digits after the decimal. Pi, accurate to 10 decimal places, is 3.1415926536.
To round this to the third decimal, note that 1 is the third number in the decimal series. The number following it is 5, and the number after the 5 is not zero. This is an indication to round up, so the 1 should become 2, making pi rounded to three decimal places 3.142.
Example 2: The square root of 2 is a number that scientists often encounter. Here it is to 10 decimal places: 1.4142135623.
Note that the third number in the decimal series is 4, and the number after it is 2. Because 2 is less than 5, the third number should be rounded down, which means leaving the 4 unchanged: 1.414.