Theory:

General rule: Rounding each factor of product/quotient of numbers to its greatest place, then multiply/divide the rounded off factors.
Example:
1. Estimate: \(387 × 42\)
 
Let us round of \(387\) and \(42\) separately and then multiply to get the answer.
 
Consider \(387\),
 
It is a three digit-number. We can round off this to a maximum of the nearest \(100's\).
 
Let us round off \(387\) to \(100's\).
 
Let us follow the steps to find the estimated number.
 
Step
Applying it
\(387\) to hundreds
1Find the digits to the hundreds place\(3\)87
2Determine the digit to its right.\(3\)87
3If this digit is \(5\) or greater add \(1\) to it.  If it is lesser, then leave it as it is.
\(3\)87
(\(8>5\)). Add \(1\) to it.
4Make the digits to the right of hundreds place \(5\) to zeros.400
 
Thus, estimating the number \(387\) to the nearest hundreds is \(400\).
 
Consider \(42\),
 
It is a two-digit number. We can round off this to a maximum of the nearest \(10's\).
 
Let us round off \(42\) to \(10's\).
 
Let us follow the steps to find the estimated number.
 
Step
Applying it
\(42\) to tens
1Find the digits to tens place\(4\)2
2Determine the digit to its right.\(4\)2
3If this digit is \(5\) or greater add \(1\) to it.  If it is lesser, then leave it as it is.
\(4\)2
(2<5). Leave it as it is.
4Make the digits to the right of tens place \(5\) to zeros.40
 
Thus, estimating the number \(42\) to the nearest tens is \(40\).
 
Now multiply the estimated numbers.
 
That is \(400 × 40 = 16000\).
 
Therefore, the estimated product is \(16000\).
 
The actual product is \(387 × 42 = 1596\). Thus, the estimated product is roughly nearer to the actual product.
 
Therefore, it is a meaningful estimation.
 
 
2. Find the estimated value of 5160÷392.
 
Let us round of \(5160\) and \(392\) separately and then divide to get the answer.
 
Consider \(5160\),
 
It is a four-digit number. We can round off this to a maximum of the nearest \(1000's\).
 
Now try to round off evenly by \(100's\).
 
Let us round off \(5160\) to \(100's\).
 
Let us follow the steps to find the estimated number.
 
Step
Applying it
\(5160\) to hundreds
1Find the digits to the hundreds place5\(1\)60
2Determine the digit to its right.5\(1\)60
3If this digit is \(5\) or greater add \(1\) to it.  If it is lesser, then leave it as it is.
5\(1\)60
(6>5). Add \(1\) to it.
4Make the digits to the right of hundreds place \(5\) to zeros.5200
 
Thus, estimating the number \(5160\) to the nearest hundreds is \(5200\).
 
Let us follow the steps to find the estimated number.
 
Step
Applying it
\(392\) to hundreds
1Find the digits to the hundreds place\(3\)92
2Determine the digit to its right.\(3\)92
3If this digit is \(5\) or greater add \(1\) to it.  If it is lesser, then leave it as it is.
\(3\)92
(9>5). Add \(1\) to it.
4Make the digits to the right of hundreds place \(5\) to zeros.400
 
Thus, estimating the number \(392\) to the nearest hundreds is \(400\).
 
Now divide \(5200\) by \(400\).
 
Estimated quotient.
 
13400|5200¯5200¯0¯
 
Actual quotient
 
13392|5160¯5096¯64¯
 
Thus, the estimated product is roughly nearer to the actual product.
 
Therefore, it is a meaningful estimation.