Do decimals round to the thousandth place?

Answer 1

Decimals may round to any place you like. The only rule is that if the digit after the digit you are rounding is five or above, you round up. Four or below, you round down.

For example, 3.1415 if being rounded to the nearest thousandth would be 3.142.

There is a problem with the above rule: it introduces an upward rounding bias. Consider the the digit after the one you are rounding: if it is 1, 2, 3 or 4 you round down. If it is 5, 6, 7, 8 or 9 you round up. If it is zero, you do nothing. So you are likely to round down 4 out of 9 times and round up 5 out of 9. That introduces an upward bias.

There are two possible solutions to the bias. Option 1: If the next digit is 5 you randomly round up or down. Option 2: If the next digit is 5, round the previous digit to an even number. Both solutions get rid of the bias and the second avoids the disadvantage that it is difficult for you (or someone else) to retrace your calculations.