Quick answer: 2.675 rounded to 2 decimal places is 2.68: the kept part is 2.67, the dropped digit 5 is exactly half, and half up rounds it up.
How it's calculated
Look at the part you drop. Less than half: keep the digits as they are. More than half: add 1 to the last kept digit. Exactly half: the rule decides – half up rounds away from zero (2.5 → 3 and −2.5 → −3), half to even goes to the even neighbour (2.5 → 2, 3.5 → 4). Some calculators round halves towards positive infinity instead, which gives −2 for −2.5; the two agree for positive numbers.
Half to even, also called banker's rounding, is the default in IEEE 754 arithmetic and in many accounting systems because it does not push totals up on average. Down simply cuts off the extra digits (truncation); up always moves away from zero.
Significant figures count from the first non-zero digit: 0.004567 to 2 significant figures is 0.0046, and 123,456 to 3 is 123,000. The calculator works on the exact digits you type, so 2.675 is not affected by floating-point storage (which many programs hold as 2.67499999…). For very large or small numbers see scientific notation.
Worked examples
- 2 decimal places, half up: 2.67|5 → 2.68
- Half to even: 2.5 → 2, 3.5 → 4
- 3 significant figures: 123,456 → 123,000
The four rules compared
| Number | Half up | Half to even | Down | Up |
|---|---|---|---|---|
| 2.5 → 0 dp | 3 | 2 | 2 | 3 |
| 3.5 → 0 dp | 4 | 4 | 3 | 4 |
| −2.5 → 0 dp | −3 | −2 | −2 | −3 |
| 2.675 → 2 dp | 2.68 | 2.68 | 2.67 | 2.68 |
| 2.665 → 2 dp | 2.67 | 2.66 | 2.66 | 2.67 |
Frequently asked questions
Why does my spreadsheet round 2.675 to 2.67?
Some programs store 2.675 in binary as 2.67499999…, which is just below half. This calculator uses the decimal digits you typed, so half up gives 2.68.
What is banker's rounding?
Rounding halves to the nearest even digit: 0.125 → 0.12 and 0.135 → 0.14. Over many values it avoids a bias upwards.
How many significant figures does 1,200 have?
It is ambiguous: 2, 3 or 4. Write it as 1.2 × 10³ (2 s.f.) or 1.200 × 10³ (4 s.f.) to make it clear.
How do I round to the nearest 5 or 0.5?
Divide by 5 (or 0.5), round to a whole number, then multiply back: 17 ÷ 5 = 3.4 → 3 → 15.
What is 2.675 rounded to two decimal places?
2.68. The usual half-up rule gives 2.68, and so does banker's rounding here, since 8 is even.
Should I round in the middle of a calculation?
Better not. Keep the full figures and round only the final answer, or small errors pile up along the way.