Round off to the nearest hundreds place: 9,750
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MathBot Answer:
\(9,750\) rounded to the nearest \(100\) is \(9800\).
Rounding \(9,750\) to the nearest \(100\) is equivalent to finding the integer multiple of \(100\) nearest to \(9,750\).
The two consecutive multiples of \(100\) that \(9,750\) falls between are:\[97 \cdot 100 = 9700\] and \[(97 + 1) \cdot 100 = 9800\] So:\[9700 \le 9,750 \le 9800\]
The distance from \(9,750\) to \(9700\) is \(\left| 9,750 - 9700 \right| = 50\).
The distance from \(9,750\) to \(9800\) is \(\left| 9,750 - 9800 \right| = 50\).
\(9,750\) is equally distant from \(9700\) and \(9800\). By convention, \(9,750\) is rounded up in this case. \(9,750\) rounded to the nearest \(100\) is \(9800\).
\(97\) from the above statement about consecutive multiples of \(100\) can be computed from the formula for the greatest integer \(n\) such that \(n \cdot 100 \le 9,750\): \[ n = \operatorname{floor}\left(9,750 \div 100 \right) = \operatorname{floor}\left(97.5 \right) = 97\]