Home > Pre-Algebra > Whole Numbers > Estimating Products

## Estimating Products

#### Introduction

Estimating numbers can help you find a rough answer for a number without having to do too much difficult math. What you gain in speed and ease, however, you lose in precision. Estimating a number is a great way of getting nearly the answer.

To estimate a product you will need to round the numbers to ones you are comfortable multiplying. This will make the whole process faster, giving you an estimate much quicker.

## Lesson

To make an estimate of a product, you start by rounding the numbers to their nearest 'landmark' numbers. These are numbers that are usually multiples of 10, 100, 1000 etc. (although that depends on how accurate you need to be, combined with the numbers you are comfortable multiplying).

For example, if we are asked to multiply 398 and 72, we can round them to their nearest landmark numbers:

We can round 398 to 400, and 72 to 70. That gives us a sum of:

400 x 70.

As a quick tip to multiply numbers with a lot of zeros at the end, just multiply the non-zero digits and then add the zeros back on to the result.

So, for 400 x 70, you can do 4 x 7 and then add the three zeros (two from the 400 and one from the 70) to the answer.

4 x 7 = 28 (add the zeroes back on) 28,000

Therefore, 400 x 70 = 28,000

The actual answer of 398 x 72 = 28,656, showing that our estimate was close enough to be useful.

If you have to multiply two decimals together you can follow the same process.

If we have 2.8 x 1.9, we can round both numbers to their nearest whole numbers:

3 x 2 = 6

The actual answer to 2.8 x 1.9 = 5.32, which is close to our estimate.

## Examples

$19 * 29$
$paper.numberWithRoundingDigit(19, 0);$
$paper.rounding(19, 0, 1);$
$19 \approx 20$
$paper.numberWithRoundingDigit(29, 0);$
$paper.rounding(29, 0, 1);$
$29 \approx 30$
First multiply the integers ($2$ * $3$) and get $6$
Then add the total number of zeroes in the two numbers
Since there are $2$ zeroes, we end up with $600$