Math Problem Solver

$3.7$ rounded to the nearest $1$ is $4$.

Rounding $3.7$ to the nearest $1$ is equivalent to finding the integer multiple of $1$ nearest to $3.7$.

The two consecutive multiples of $1$ that $3.7$ falls between are:$$3 \cdot 1 = 3$$ and $$(3 + 1) \cdot 1 = 4$$ So:$$3 \le 3.7 \le 4$$

The distance from $3.7$ to $3$ is $\left| 3.7 - 3 \right| = 0.7$.

The distance from $3.7$ to $4$ is $\left| 3.7 - 4 \right| = 0.3$.

$3.7$ is closer to $4$ than it is to $3$, so $3.7$ rounded to the nearest $1$ is $4$.

$3$ from the above statement about consecutive multiples of $1$ can be computed from the formula for the greatest integer $n$ such that $n \cdot 1 \le 3.7$: $$n = \operatorname{floor}\left(3.7 \div 1 \right) = \operatorname{floor}\left(3.7 \right) = 3$$