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## Estimating Differences

#### Introduction

Estimating can be a useful tactic in math. Estimating allows you to quickly get a rough answer in your head. It can also be useful to estimate so that, when you use a calculator to solve a problem, you know roughly what the answer should be in case you enter some details wrong into the calculator. If you've estimated in advance, you'll catch your mistake.

Estimating the differences between numbers involves rounding the numbers. The answer will be imprecise but may be enough for what you need.

## Lesson

To estimate the difference between two numbers, we need to round the numbers to it's nearest 'landmark'. Generally, a 'landmark' number is a multiple of 10, 100, 1000 etc., although you can make a landmark any number you are comfortable in subtracting.

For example, if we are given the sum:

897 - 412 = ?

We can start by rounding both numbers to their nearest landmark. The nearest landmark to 897 is 900. The nearest landmark to 412 is 400.

This makes the sum:

900 - 400, which equals 500.

500 is only the estimate or the rough answer. The actual answer to 897 - 412 is 485, which is close to 500.

We can also estimate differences through rounding with decimals. For example:

2.8 - 1.01 = ?

We can round both of these to their nearest 'landmark,' which in this case will be the nearest whole number.

2.8 can be rounded to 3, and 1.01 can be rounded to 1. This makes the sum:

3 - 1 = 2

The actual answer to 2.8 - 1.01 is 1.79, which is close to 2.

Estimating differences, therefore, provides us with a close (but imprecise) answer, without having to do too much tricky calculation.

## Examples

Estimate the $difference$ 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 subtract $1,500$ minus $1,100$ we get $400$