# Estimation, Approximation and Rounding | SkillsYouNeed (2023)

Sometimes, you may find it helpful to know the approximate answer to a calculation.

You may be in a shop and want to know broadly what you’re going to have to pay.

You may need to know roughly how much money you need to meet a couple of bills.

You may also want to know roughly what the right answer to a more complicated calculation is likely to be, to check that your detailed work is correct.

Whatever your precise need, you want to know how to estimate or approximate the right answer.

## Rounding

One very simple form of estimation is rounding. Rounding is often the key skill you need to quickly estimate a number. This is where you make a long number simpler by ‘rounding’, or expressing in terms of the nearest unit, ten, hundred, tenth, or a certain number of decimal places.

For example, 1,654 to the nearest thousand is 2,000. To the nearest 100 it is 1,700. To the nearest ten it is 1,650.

The way it works is straightforward:you look at the number one place to the right of the level that you are rounding to and see whether it is closer to 0 or 10.

In practice, this means that if you’ve been asked to round to the nearest 10, you look at the units. If you are rounding to three decimal places, you look at the fourth decimal place (the fourth number to the right of the decimal point) and so on. If that number is 5 or over, you round up to the next number, andif it is 4 or under, you round down.

Round Up or Round Down?

We round numbers to reduce their number of digits while keeping the result as close to the original number as possible.

Numbers that are less than 5 get rounded down.

Numbers that are 5 or higher get rounded up.

Rounding to one decimal place:

• 1.47 rounds to 1.5
• 1.42 rounds to 1.4
• 1.4535412 rounds to 1.5
(Video) Approximation & Estimation | Numbers | Maths | FuseSchool

### Rounding: Worked Examples

#### Example 1

Express 156 to the nearest 10

In this example you look at the tens and units. The hundreds will not change. You need to decide whether 56 will be rounded up to 60 or down to 50.

Looking at the units, you know that 6 is more than 5, so you round up.

#### Example 2

Express 0.4563948 to three decimal places.

As you're working to three decimal places, the answer will start 0.45 and you need to determine the third number after the decimal point

To work out whether the third number is 6 or 7, you need to look at the fourth number, which is 3. As 3 is less than 5, you round down.

(Video) Approximations to Calculations - Corbettmaths

You can use the technique of rounding to start estimating the answer to more complex problems.

## Estimation

Estimating can be considered as ‘slightly better than an educated guess’. If a guess is totally random, an educated guess might be a bit closer.

Estimation, or approximation, should give you an answer which is broadly correct, say to the nearest 10 or 100, if you are working with bigger numbers.

Probably the simplest way to estimate is to round all the numbers that you are working with to the nearest 10 (or 100, if you are working in thousands at the time) and then do the necessary calculation.

For example, if you are estimating how much you will have to pay, first round each amount up or down to the nearest unit of currency, pound, dollar, euro etc. or even to the nearest 10 units (£10, \$10, €10), and then add your rounded amounts together.

Many stores like to give prices ending in .09 and especially 0.99. The reason for this is that a shirt that costs 24.99 'sounds' cheaper than one that costs 25.00. When shopping for numerous items it can be useful to keep a running tally, an estimate of the total cost, by rounding items to the nearest currency unit, £, \$, € etc.

If you are trying to work out how much carpet you will need, round the length of each wall up to the nearest metre or half-metre if the calculation remains simple, and multiply them together to get the area.

Warning!

If you are relying on your calculation to make sure that you have enough of something, whether money or carpet, always round up. That way you will always over-estimate. Even engineers take this approach when thinking about the design of a structure before doing a detailed specification. It’s better to have a component that’s a bit stronger than it needs to be than one that is too weak.

#### Example 1

You want to buy carpet for two rooms. The first is 3.2m by 2.7m. The second is smaller, 1.16m by 2.5m. How much carpet do you need to buy to be sure of having enough for both rooms?

(Video) How to Estimate in Maths #21

The first room is approximately 3m by 3m, which is 9m2.

The second is just over 1m by 2.5m. Strictly speaking, you would round this to 1m by 2.5m, or 2.5m2.

In total, then, that’s 11.5m2. It’s hard to buy carpet in anything except whole m2, so you’ll need to round up to 12m2. In each case, you have rounded up one of the numbers by more than you have rounded the other one down, so you’re probably fine.

A quick check with a calculator will, indeed, confirm that you need exactly 11.54m2. 12m2 will be plenty.

#### Example 2

You’ve decided to add another room to the carpet buying. The last room is 3.9m by 2.2m. How much carpet do I need for all three rooms?

3.9m is rounded up to 4m. 2.2m rounds down to 2m.

2 × 4 is 8m2, which gives a total, for all three rooms of 20m2.

However, in rounding down to 2m, you have taken out 0.2m. In rounding up to 4m, you have only added 0.1m.

You may not order quite enough carpet although you might get away with it because you rounded up to 12m2 for the first two rooms.

However, to be absolutely sure, you probably want to round 2.2m up, to 2.5m.

Multiply 2.5 by 4 to get 10m2. This means you need 22m2 of carpet for all three rooms.

A quick check with a calculator will confirm that 20m2 is not quite enough: You need 20.9m2 exactly.

Need a refresher on how to calculate area? See our page Calculating Area for help.

### Estimated Time of Arrival (ETA)

Estimated time of arrival is used frequently used when travelling. Trains, buses, planes, ships and in-car satellite navigation (sat-nav) all use ETA.

(Video) Estimation

The ETA is based on distance and speed of travel, it is ‘estimated’ because it cannot take into account changes to speed during the journey. Your flight may arrive early because of favourable tail winds. Your road trip may take longer than expected because of traffic.

The ETA is usually calculated by a computer and can change during your trip. As you near your destination, more data becomes available so the estimated time that you will arrive becomes more accurate.

### A Special Case: Estimating for Work

You will almost certainly come across ‘estimates’ for work to be done, whether from a builder, plumber, mechanic or other tradesperson.

In this case, the tradesperson concerned has probably estimated how much time they are likely to take to do the work, multiplied it by their hourly or daily rate, and perhaps added additional charges for materials or a call-out.

They may also have added a ‘contingency’ for extra work needed, which is likely to be 10 or 20%, and will mean that you are not unpleasantly surprised by the bill if they find something unexpected that needs fixing.

An ‘estimate’ is not legally binding. It is just what it says: an estimate.

However, a ‘quote’ or ‘quotation’ for work done is legally binding on cost, provided that the work done is what was quoted for. However, if you have asked for extra work: ‘just add that bit’ or ‘do that while you’re here’, don’t be surprised if the bill is larger than you were expecting.

### A Useful Skill

You may be wondering why you’d ever use estimation when you have a calculator on your phone.

The ability to estimate will mean that you will know if the answer you get from the calculator is not right, and do it again.

Continue to:
Mental Arithmetic – Basic Mental Maths Hacks
Real World Maths

Also see:
Probability an Introduction | Special Numbers and Concepts
Percentages | Percentage Change | Averages (Mean, Median and Mode)

(Video) Learn the Basics of Estimation, Approximation, and Rounding Numbers in Maths l Introduction To Math

## FAQs

### How much do you round to when estimating? ›

In order to estimate a number: Round each number to 1 significant figure. symbol ≈ . Calculate using the rounded numbers to give an approximate answer and consider units in the answer.

What is an approximation answer? ›

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations .

What is estimation with example? ›

Estimation its often done by sampling, which is counting a small number of examples something, and projecting that number onto a larger population. An example of estimation would be determining how many candies of a given size are in a glass jar.

What are 4 techniques of estimation? ›

Major project estimation techniques
• Top-down estimate. ...
• Bottom-up estimate. ...
• Expert judgment. ...
• Comparative or analogous estimation. ...
• Parametric model estimating. ...
• Three-point estimating.
27 Apr 2022

How do you estimate correctly? ›

Tips on better estimating time for tasks
1. Time your tasks. Spend a week or longer tracking how long it takes to complete everything you do. ...
2. Use a fudge ratio. ...
3. Overestimate your time requirements. ...
5. Use a three-point estimation. ...
6. Get feedback. ...
7. Use time tracking apps. ...
8. Estimate someone else's time.
15 Jun 2021

What is the rule for estimating? ›

General Rule of Estimating

When it comes to estimating in math, there is a general rule for you to follow. This general rule tells you to look at the digit to the right of the digit you want to estimate, and if it is less than 5 then you round down, and if it is greater than 5, you round up.

What is the rule of approximation? ›

look at the first digit after the decimal point if rounding to one decimal place or the second digit for two decimal places. draw a vertical line to the right of the place value digit that is required. look at the next digit. if the next digit is 5 or more, increase the previous digit by one.

What are the 3 main types of estimates? ›

There are three types of estimates that can be used to communicate costs to clients, including ballpark, budgetary, and definitive.

How do you write an estimate example? ›

What to include in a job estimate
1. Company contact info.
2. A project description/overview of the services you'll provide.
3. The related cost of materials required to deliver the services.
4. What will not be included in the project.
5. Project timelines and completion dates.
6. Total cost of services.
7. Payment terms.
8 Apr 2021

What are the two types of estimation? ›

There are two types of estimates: point and interval. A point estimate is a value of a sample statistic that is used as a single estimate of a population parameter.

### What are the five 5 main stages of an estimate? ›

Let's take a more in-depth look at each level in the construction estimating process.
• Level 1: Order of magnitude estimate.
• Level 2: Schematic design estimate.
• Level 3: Design development estimate.
• Level 4: Construction document estimate.
• Level 5: Bid estimate.

What are the types of estimation? ›

• Preliminary estimate. The preliminary estimate is a rough estimate given to give a general idea about how much a total project will cost. ...
• Detailed estimate. As the scope of the project is better known, one can take out a detailed estimate. ...
• Quantity estimate. ...
• Bid estimate. ...
• Cost estimates.
8 Apr 2022

What are the 5 principles of estimating? ›

Principles Of Estimating
• Tender schedules.
• Non-Price Criteria & Priced Criteria.
• Direct Pricing & Indirect Pricing.
• Estimating (rating) methods including First Principles, Second Principles & Bench Marking.
• Cost Planning.
4 Jun 2019

How do I get better at estimating? ›

1. Double your initial guess. Most of us are optimists. ...
2. Hindsight is 20/20. ...
3. Don't eat more than you can chew. ...
4. Identify what's subjective. ...
5. Never assume anything. ...
6. Don't offer free estimates.

What is the most accurate way to estimate? ›

An analytic estimate (also called bottom-up estimating) is one of the most accurate cost estimation techniques—but it can also be time-intensive. Bottom-up estimating breaks the project down into smaller parts and then creates cost estimates for those variables.

What is 1st principle in estimating? ›

First Principles Estimate means a cost estimate derived by calculating the cost of each item of a project by multiplying the quantity of work by historical unit rates. The project cost is then determined by the sum of the elemental costs.

What is rule of thumb in estimating? ›

A rule of thumb method in cost estimating is drawn from design or practical experience and it provides a rough guide to come up with quantities during the initial stages of design like the concept or schematic phases. The rule of thumb is a method for developing quick approximate estimates of costs.

What is method of approximation? ›

An approximation method enabling to solve the many body Schrödinger equation (H-E)Ψ=0 consists in transforming this partial differential equation into an infinite set of one dimensional coupled differential equations, a finite number of which being afterward numerically integrated.

What is the difference between estimation and approximation? ›

An estimation is the act of estimating, or guessing, about the quantity, quality, or other aspect of an object or person. An approximation can be an object or person that is almost exactly like something else, but not quite, either by defect or design.

What is the formula for approximation? ›

The linear approximation formula is based on the equation of the tangent line of a function at a fixed point. The linear approximation of a function f(x) at a fixed value x = a is given by L(x) = f(a) + f '(a) (x - a).

### What are the method of approximate estimation? ›

Methods of Approximate Estimate:

Plinth area method. Cubic rate method. Approximate quantities with bill method. Service unit method.

Which method is used for approximate estimation? ›

Explanation: There are various methods used for preparing approximate estimates. These are the plinth area method, unit base method and cubical contents method.

What is approximate estimate method? ›

Approximate Estimate: The other name of Approximate estimate is preliminary or rough. estimate. This is made to find out an approximate cost in a short time and thus enable the responsible. authority concemed to consider the financial aspect of the scheme for according sanction to the same.

How do you use approximation rule? ›

Approximate a value for the variable that will simplify the equation. Simpify the equation and solve for the variable. Using the result, make a second approximation. Repeat the process until a constant value is obtained.

How do you find a approximate number? ›

For example, 1,654 to the nearest thousand is 2,000. To the nearest 100 it is 1,700. To the nearest ten it is 1,650. The way it works is straightforward: you look at the number one place to the right of the level that you are rounding to and see whether it is closer to 0 or 10.

What is a estimation and approximation? ›

An estimation is the act of estimating, or guessing, about the quantity, quality, or other aspect of an object or person. An approximation can be an object or person that is almost exactly like something else, but not quite, either by defect or design. If by design, it is not meant to be exact.

How do you round and approximate? ›

Rounding numbers to the nearest 10, 100, 1,000

To approximate to the nearest ten, look at the digit in the tens column. To approximate to the nearest hundred, look at the digit in the hundreds column. For the nearest thousand, look at the digit in the thousands column.

What is the need for approximate estimation? ›

Approximate estimate, also known as preliminary or rough estimate, helps to find out the approximate cost of a project in a very short time. Moreover, it enables the concerned authority to consider the financial aspect of the scheme to accord sanction to the same.

What are the two methods of estimation? ›

Types of estimation methods
• Top-down estimation. ...
• Bottom-up estimation. ...
• Three-point estimation. ...
• Analogous estimation. ...
• Parametric estimation. ...
• Expert judgment.
18 Apr 2022

Which one is the types of estimation? ›

Approximate Quantity Method Cost Estimate. Detailed Cost Estimate. Revised Cost Estimate. Supplementary Cost Estimate.

### Which is the most correct estimate? ›

A detailed estimate is the most accurate method and consists of working out the quantities of each item of works and working the cost. The dimensions are taken directly from the drawings and quantities of each item are calculated.

What are the five different types of estimates? ›

There are five main types of construction cost estimates: preliminary, detailed, quantity, bid, and control. Each is used for a different purpose at a different time in a project lifecycle.

Which is more accurate method of approximate estimating? ›

Explanation: Detailed estimate: A detailed estimate should have documents such as report, specifications, drawings/plans, design charts and schedule of rates and is the most accurate method of estimating.

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