Question

How do you round to the nearest unit ?

Answer 1

See below

Explanation:

Rounding to the nearest unit means to find the nearest integer to a given number.

Basically, you have to get rid of the decimal part, if any.

As an immediate corollary, you have that if a number `x` is already an integer, then there's no point in rounding it, since the result would be `x` itself.

Now, let's assume that our number actually has a decimal part, for example `4.687`.

It might help you to think of this number as `4+0.687` to clearly see that 4.687 lies between `4` and `5`, since it is something (`0.687`) more than `4`, but still not `5`.

So, the question is: is our number closer to `4` or to `5`? Which, in turn, means to ask: the decimal part that we've added, `0.687`, is nearest to `0` or `1`?

If it is nearest to `0`, it means that our number is more than `4`, but still nearer to `4` than it is to `5`, otherwise it is "far enough" from `4` to be nearer to `5`.

Since halfway between `0` and `1` is `0.5`, and our decimal part is `0.687>0.5`, we can say that `4.687` is rounded to `5`.

I'll leave some more examples:

• `0.3345 \to 0`
• `-5.178\to -5`
• `-7.95 \to -8`
• `20 \to 20`
• `20.687 \to 21`