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# A Note on Rounding

Reference > Science > Significant Figures

The standard method that most students are taught for rounding is: if the digit to be rounded is 5 or more, round up. This rule gives the following results for rounding numbers to the nearest tenth:

1.22 rounds to 1.2
1.25 rounds to 1.3
1.27 rounds to 1.3

There is another rule, however, which is occasionally used instead of this rule; it is called the "Half to Even" rule. This rule states that if the last digit is greater than 5, you round up, but if the last digit is equal to 5, you round to the nearest even number. That would make the examples above look like this:

1.22 rounds to 1.2
1.25 rounds to 1.2
1.27 rounds to 1.3

The change is in rounding 1.25; it no longer rounds to 1.3, it rounds to 1.2, because 2 is even.

On the other hand, 2.75 would round up to 2.8, because 8 is even.

Note that any non-zero digit after the 5 means that you round up. Thus, 2.65 rounds to 2.6, while 2.651 rounds to 2.7.

If you're wondering why a rule like this would exist, the answer is that it's basically a way of randomizing (and hopefully decreasing) round-off error. If you have a series of numbers you're working with that all end in five, and you round all of them, rounding them all upÂ will result in an answer that is skewed in the upward direction. On the other hand, if you're using the half-to-even rule, odds are good that some of those will round down instead of up, decreasing your overall rounding error.

Most teachers will expect you to use the "round-up" rule rather than the "half-to-even" rule, but it's worth checking with your teacher to make sure.

## Questions

1.
Round 1.05 to the nearest tenth, using the half-to-even rule.
2.
Round 1.051 to the nearest tenth, using the half-to-even rule.
3.
Round 1.15 to the nearest tenth, using the half-to-even rule.
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