Algebra Tutorials!
   
 
 
Tuesday 19th of March
 
   
Home
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Percents
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Algebra
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
fractions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Quadratics
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Decimals
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
   
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Rounding Numbers

Question: What is 14 489 to the nearest 1000?

Misconception

To obtain the answer, round to the

nearest 10, 100 and then 1000; thus:

14 489 to the nearest 10 is 14 490,

14 490 to the nearest 100 is 14 500,

14 500 to the nearest 1000 is 15 000.

Hence: the misconception leads to the incorrect answer, 15 000.

Correct

The answer must be either 14 000 or 15 000, and since

14 489 - 14 000 = 489,

whilst

15000 - 14 489 = 511,

clearly 14 489 is nearer to 14 000 than to 15 000.

Hence: the correct answer is 14 000.

 

Further Explanation

The correct explanation above, that 14 489 is nearer to 14 000 than to 15 000, is clear-cut; but why is the 'misconceived' method wrong?

This is best illustrated by taking another example and putting it into context.

Two stations, A and B, are 500 metres apart:

You stand between the stations, 245 m away from A and 255 m from B and you want to walk to the nearest station. Naturally you turn left and walk 245 m.

But now imagine there are five trains parked between the stations, each train 100 m long, and each divided into 4 carriages of equal length.

Your position, 245 m away from A, is now 20 m along the second carriage of the third train, and you decide to find your way to the nearest station by first asking which is the nearest carriage-end (the one on the right, 250 metres from A). Having moved there, you then seek the nearest end of the train , which (as, by convention, we round mid-points up) is to the right at 300 metres from A. From there finally, you go to the nearest station , and this time arrive at B.

Clearly the result is wrong. Why?

Because when you want to find the nearest station , the questions about the nearest carriageend and the nearest train end are irrelevant. Doing it this way might not matter in some cases, but here it does. The unnecessary interim steps move you away from your starting point, and here, in the wrong direction. Another instructive point: this exercise provides an opportunity to distinguish between an arbitrary convention (i.e. which way to go from the middle) and a reasoned choice (i.e. the correct approach to round).

Copyrights © 2005-2024