Math Problem Solver

$1.54$ rounded to the nearest $1$ is $2$.

Rounding $1.54$ to the nearest $1$ is equivalent to finding the integer multiple of $1$ nearest to $1.54$.

The two consecutive multiples of $1$ that $1.54$ falls between are:$$1 \cdot 1 = 1$$ and $$(1 + 1) \cdot 1 = 2$$ So:$$1 \le 1.54 \le 2$$

The distance from $1.54$ to $1$ is $\left| 1.54 - 1 \right| = 0.54$.

The distance from $1.54$ to $2$ is $\left| 1.54 - 2 \right| = 0.46$.

$1.54$ is closer to $2$ than it is to $1$, so $1.54$ rounded to the nearest $1$ is $2$.

$1$ from the above statement about consecutive multiples of $1$ can be computed from the formula for the greatest integer $n$ such that $n \cdot 1 \le 1.54$: $$n = \operatorname{floor}\left(1.54 \div 1 \right) = \operatorname{floor}\left(1.54 \right) = 1$$