Rounding Doubt

Main Question or Discussion Point

Hi everyone, i didn't understand how to round up a number when i'm having a five,
for example if i have a number with the last digit greater than 5 like 12.76 i know that i can round up to 12.8 and if the last digit is less than 5 for example 12.74 i know that i can round up like this 12.7, but i didn't understand how to round up if i have a number like this : 12.65.

my book says:
" If the last digit dropped is equal to 5, the remaining digit should be rounded to the nearest even number. (This helps avoid accumulation of errors in long arithmetic
processes.)"

Can you explain me what is the meaning (english is not my mothertongue)? I can't understand it, and can you make me some examples ? please

Related Other Physics Topics News on Phys.org
even = pari
odd = dispari

jbriggs444
Homework Helper
2019 Award
The rule means that 3.5 should be rounded up to 4 (an even number) and that 2.5 should be rounded down to 2 (an even number).

The idea is that if you consistently follow this rule, you are likely to round up and down with equal frequency. If you always rounded up when the last digit is five then long calculations would tend to produce results that are too high. If you always rounded down when the last digit is five then long calculations would tend to produce results that are too low.

Rounding to an even number tends to balance things out.

thank you very much!! now I understand how it works! Thank you!

mfb
Mentor
Rounding to an even number tends to balance things out.
Rounding to an odd number or throwing dice would do the same. But the even numbers have another advantage: You can divide by 2 afterwards (if that is required in some way), and do not need to round again.

3.5 => round to 4 => divide by 2 => 2
3.5 => round to 3? => divide by 2 => 1.5 => round to what? 2 is better than 1.

2.5 => round to 2 => divide by 2 => 1
2.5 => round to 3? => divide by 2 => 1.5 => round to what? 1 is better than 1.