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Estimating Sums

Introduction

Estimating is a way of solving an equation that favors ease and speed over accuracy. Most of the time in math, it's more important to get the correct answer than to get the answer quickly. However, sometimes, it's ok to get a rough number or to solve an equation quickly. In these cases, we can use estimation.

The best way to estimate the answer to a sum is to use rounding to convert the sum into numbers that are easier to work with.

Lesson

To estimate the sum of two numbers, we need to first round them to their nearest 'landmark number.' A 'landmark number' is usually a multiple of 10, 100 or 1000. These numbers are easier to add together. For example, 4,086 can be rounded to its landmark of 4,000.

Once we've rounded, we can then estimate the sum of the numbers by adding the rounded numbers. For example, if we were given the sum:

8,987 + 406 = ?

We could round the numbers to their nearest landmarks. 8,987 becomes 9,000 and 406 becomes 400. That gives us:

9,000 + 400 = ? 9,000 + 400 = 9,400

By estimating, therefore, we have got an answer of 9,400. The actual answer to 8,987 + 406 = 9,393, so our estimate was only 7 away.

If you are dealing with decimals, then your 'landmark numbers' can be the nearest whole number.

For example, if you are given 18.9 + 12.01, you can round the numbers to 19 and 12 respectively. This would give an answer of 31.

Examples

Estimate the $sum$ by first rounding each number to the nearest $hundred$
$1,530 \text{+} 1,111$
$paper.numberWithRoundingDigit(1530, 1);$
$paper.rounding(1530, 1, 2);$
$1{,}530 \approx 1{,}500$
$paper.numberWithRoundingDigit(1111, 1);$
$paper.rounding(1111, 1, 2);$
$1{,}111 \approx 1{,}100$
When we add $1,500$ and $1,100$ we get $2,600$