Rounding and cutting are not the same operation, and mixing them up costs money in long columns. The TRUNC function removes the decimals instead of weighing them.
Rounding asks which whole number is nearest. Cutting asks nothing at all, since it simply stops reading once it has taken what you wanted.
For instance, an hours column that should never round upward wants the second behaviour. So does anything where a fraction of a unit is not yet a unit you can bill for.
The TRUNC function.
Point it at a number and the fraction disappears.
=TRUNC(A2)
Nothing is weighed and nothing is nudged. Therefore 8.9 becomes 8, which is the answer ROUND would never give you, because ROUND would see that the nine is closer to nine.
A second argument keeps some of the decimals. In short, the TRUNC function with =TRUNC(A2,2) keeps two of them, so 8.987 becomes 8.98 rather than the 8.99 that rounding produces.
It disagrees with INT on negatives.
INT looks like the same function and behaves like it on every positive number you will ever test with. That is exactly why the difference gets shipped.
=INT(A3)
The two part company below zero. Cutting moves toward zero, so -2.7 becomes -2, while INT always moves down, which makes the same input -3.
Consequently a column of refunds, adjustments or temperature readings can disagree with itself by a whole unit per row. Meanwhile every positive row above it agrees perfectly, which is what keeps the bug hidden.
Result of the TRUNC function.
Before. One positive value and two negative ones, with nothing cut yet.
After. The two functions agree once and disagree twice.
A2 -> 8.9 A3 -> -2.7 A4 -> -0.4 =TRUNC(A2) -> 8 =INT(A2) -> 8 =TRUNC(A3) -> -2 =INT(A3) -> -3 =TRUNC(A4) -> 0 =INT(A4) -> -1 =TRUNC(8.987,2) -> 8.98 =ROUND(8.987,2) -> 8.99
The last two lines are worth reading twice. Same input, same number of decimals kept, and a penny of difference that multiplies by however many rows the sheet happens to have.
Every one of these changes the stored value rather than the display. ROUND covers that distinction, and it is the reason a number format and a formula are not interchangeable.