Math Problem Solver

\(3215.7\) rounded to the nearest \(100\) is \(3200\).

Rounding \(3215.7\) to the nearest \(100\) is equivalent to finding the integer multiple of \(100\) nearest to \(3215.7\).

The two consecutive multiples of \(100\) that \(3215.7\) falls between are:\[32 \cdot 100 = 3200\] and \[(32 + 1) \cdot 100 = 3300\] So:\[3200 \le 3215.7 \le 3300\]

The distance from \(3215.7\) to \(3200\) is \(\left| 3215.7 - 3200 \right| = 15.7\).

The distance from \(3215.7\) to \(3300\) is \(\left| 3215.7 - 3300 \right| = 84.3\).

\(3215.7\) is closer to \(3200\) than it is to \(3300\), so \(3215.7\) rounded to the nearest \(100\) is \(3200\).

\(32\) from the above statement about consecutive multiples of \(100\) can be computed from the formula for the greatest integer \(n\) such that \(n \cdot 100 \le 3215.7\): \[ n = \operatorname{floor}\left(3215.7 \div 100 \right) = \operatorname{floor}\left(32.157 \right) = 32\]