Estimate the products or quotients — lesson. Mathematics State Board, Class 6.

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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
1	Find the digits to the hundreds place	$3$ 87
2	Determine the digit to its right.	$3$ 87
3	If 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.
4	Make 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
1	Find the digits to tens place	$4$ 2
2	Determine the digit to its right.	$4$ 2
3	If 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.
4	Make 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

$5160 \div 392$ .

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
1	Find the digits to the hundreds place	5 $1$ 60
2	Determine the digit to its right.	5 $1$ 60
3	If 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.
4	Make 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
1	Find the digits to the hundreds place	$3$ 92
2	Determine the digit to its right.	$3$ 92
3	If 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.
4	Make the digits to the right of hundreds place $5$ to zeros.	400