Estimate the product \(758 \times 6784\) using the general rule.
\(\approx 5{,}600{,}000\)
General rule: Round each number to its highest place value, then multiply.
Find highest places:
For \(758\): highest place is hundreds.
For \(6784\): highest place is thousands.
Round \(758\) to the nearest hundred:
Hundreds digit: \(7\)
Tens digit: \(5\)
Since \(5\ge 5\), round up.
So, \(758\approx 800\).
Round \(6784\) to the nearest thousand:
Thousands digit: \(6\)
Hundreds digit: \(7\)
Since \(7\ge 5\), round up.
So, \(6784\approx 7000\).
Multiply the rounded numbers:
\(800\times 7000\)
Write in factors: \(800=8\times 100\), \(7000=7\times 1000\).
\((8\times 100)\times(7\times 1000)\)
\(=(8\times 7)\times(100\times 1000)\)
\(=56\times 100000\)
\(=5{,}600{,}000\)
Estimated product: \(\approx 5{,}600{,}000\).