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Estimation in Real Life

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Vectors in Space
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
- 3 Dimensional Vectors
- 3-Dimensional Figures
- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
- Area of Circular Sector
- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
- Trapezoids
- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Point Estimation
- Probability
- Probability Calculations
- Probability Distribution
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- Quantitative Variables
- Quartiles
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- Survey Bias
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
- Type I Error
- Type II Error
- Types of Data in Statistics
- Venn Diagrams

I recall a while ago, Imisi was asked to give the cost of getting ice cream for 11 players of our high school if the cost of ice cream was £2.8. Immediately, she responded almost without thinking, "approximately £33".

That was cool to us because we all were expecting her to have used the calculator on her phone.

Being smart is cool and hereafter, we are going to be discussing estimation in real life.

Estimation is a process that involves giving answers which are not the same as the exact value by calculation when using the main figures but is close to the exact value. This may or may not be achieved by calculation.

Sometimes, you may not need a precise answer but you need a number close to it so that you can carry out a task.

For instance, if you were to make a quick budget on transportation to a place to and from and the cost of a trip is £5.7, surely, you would make a budget of £12. By approximating or rounding up 5.7 to 6 and multiplying by 2.

Note that estimations can take place without necessary calculating.

For instance, if you were to make a report on the number of people leaving Frimley in a discussion, the exact population is 6178. It would be easier to say, "About 6,000 people leave in Frimley".

Note that there was no operation involving addition, subtraction, multiplication, or division before you made your estimate.

When we estimate in math, we use the symbol '**≈**' which means "**almost equal to**" or '**≅**' which means "**approximately equal to**".

Estimate value is the value arrived at with or without calculation that lacks precision.

For example, 500 is an estimate of 483. Similarly, 600 is an estimate of the product between 3.8 and 148.

The exact value is the main value which in itself is accurate and precise.

For example, if the population of a place is 697, the exact value is 697 but the estimate is 700.

Likewise, when calculating the product between 3.8 and 148, the exact value is 562.4 but its estimated value could be 600.

Real-life estimation has a great deal of importance as it is used in our day-to-day activities. The following are some of the importance of real-life estimation.

Instead of bothering yourself arriving at a precise value, estimation takes that burden and makes the provision of answers faster.

Recall Imisi's scenario at the beginning of this article, estimation enabled her to provide answers without much thinking or using a calculator.

This means that for quick responses in figures that do not bother about precision or exactitude which may or may not require calculation, you should estimate to save time.

Even though estimates are not exact in relation to the real answer, it gives us an idea of what the answer should be like.

When we eventually make calculations either by solving with a pen and paper or using devices like a calculator and get something weird or entirely different from our estimate we know something has gone wrong.

For instance, if you were to add 2345 to 3211 and use a calculator you arrived at 2556. Surely, by your estimate, you should be getting something above 4000.

Because you are aware of that, you would then check your calculator and notice that rather than typing 3211, you typed 211. Without having an estimate beforehand, it would be had to spot errors.

Most budgets made are rough estimates of cost. Without estimates, budgeting may even be impossible. Because estimates in budgets take into account other miscellaneous events that may hike the exact expenditure in carrying out a project.

For instance, Finicky built a house in 2009 for £250,000. If Kohe, his son, wishes to build the same house 3 years after, he would have to make an estimate of about £300,000 per peradventure because there are other factors that may increase his expenditure on the house.

This stands to be the reason why estimations are generally used in the business world.

This is not exhaustible as various fields have their need for estimation tailored to their activities.

Estimation has several uses considering how important it is as earlier described. Its uses are found in several fields but we shall emphasize only its real-life application in math.

In mathematics, in order to apply estimates, students are taught approximation so that numeric data is easily presented. Its application in approximation can be before or after an operation is carried out.

On one hand, a typical example of its application after an operation is carried out is when 100% is to be divided amongst 3 people and your answer is 33.3333333333...3%. It would be ridiculous to write those endless 3 so you may just want to say, "approximately 33%". In this case, you estimated after calculating.

On the other hand, if you were to find the area of a rectangular lawn measuring 9.8m by 4.2m, you found the product between 10m and 4m to arrive at 40m^{2}, then your estimation was done before the calculation.

Being aware of the importance and uses of estimation, you would need to know how to estimate. The following rules would be beneficial in carrying out estimation.

a) Always tend to approximate to the highest or second to the highest place value. This would make subsequent calculations faster. However, beware that the higher the place value, the farther difference between your estimate and the exact value.

For example, 56 784 can be approximated to 60 000 which is the highest place value, or 57 000 which is the next highest place value. This is advisable because it is easier to find the product between 60 000 and 3 than 56 880 and 3.

b) When estimating, if the digit closest (rightwards) to the main digit (whose place value is of your interest) is less than 5, then leave the digit and convert the other digits after your main digit to 0.

For example, in 56317, you wish to estimate to the nearest thousand, then 6 is your main digit and the next number to the right after 6 is 3 but it is less than 5. So my estimate becomes 56000.

c) When estimating, if the digit closest (rightwards) to the main digit (whose place value is of your interest) is greater than 5, then increase the main digit by 1 and convert the other digits after your main digit to 0.

For example, in 56317, you wish to estimate to the nearest ten thousand, then 5 is your main digit and the next number to the right after 5 is 6 which is greater than 5. So my estimate becomes 60000.

Since you know the rules to follow before estimation, you should apply them to the following examples.

Ireti is a news reporter and she wishes to give an estimate of the following populations to the nearest thousand,

a) Reading - 347,510

b) Aldershot - 37,131

c) Farnborough - 65,034

**Solution**

If you apply the earlier explained rules, your answer for this task would be,

a) Reading - 348,000.

This is because the digit occupying the thousand position is 7 and the digit in the next lower place value (hundred) is 5. Remember that the digit in the next lower place value needs to be equal to or greater than 5 to round up the next digit. This is why **7 ****is rounded up to 8**. So the population of Reading is approximated to 348,000.

b) Aldershot - 37,000.

This is because the digit occupying the thousand position is 7 and the digit in the next lower place value (hundred) is 1. Remember that the digit in the next lower place value needs to be equal to or greater than 5 to round up the next digit. This is why **7**** is not rounded up to 8**. So the population of Aldershot is approximated to 37,000.

c) Farnborough - 65,000

This is because the digit occupying the thousand position is 5 and the digit in the next lower place value (hundred) is 0. Remember that the digit in the next lower place value needs to be equal or greater than 5 to round up the next digit. This is why **5**** is not rounded up to 6**. So the population of Aldershot is approximated to 65,000.

Find to the nearest thousand cubic meters, the volume of a cuboidal tank measuring 63m by 28m by 11m.

**Solution**

We recall that the volume of a cuboid is given by

In this question, neither the length, breadth nor height was specified, and looking at the formula, the specification does not really matter. So we use an estimate of each dimension to get our volume in the nearest thousand cubic meters.

Thus, we can approximate the length, breadth and the height to

And thus the volume will be approximated to,

- In math, estimation is a process that involves giving answers which are not the same as the exact value by calculation using the main figures but is close to the exact value.
- The estimated value is the value arrived with or without calculation that lacks precision.
- The exact value is the main value which in itself is accurate and precise.
- Estimation is important because it makes us give quicker responses, easily spot errors, and in budgeting.
- There are several rules that need to be followed before estimation is done correctly.

In mathematics, there are two basic methods of estimation which is rounding up and rounding down.

Estimation is applied in real life in budgeting, engineering, statistics, etc.

More about Estimation in Real Life

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