Learning Futures
-
Teaching Support
- - Technology-Enabled Learning
- - WOS Studio
-
- MESH
- - Events, Workshops and Programs
- - Resources by Discipline
-
- Support and Resources by Topic
- - Statistics Help (General)
- - Statistics Help (R Commander)
- - Arithmetic
- - Standard Derivatives
- - Standard Integrals
- - Hyperbolic Trigonometric Functions
- - Remainders and Quotients
- - SPSS Help
- - Logic Basics: AND, OR, NOT
- - Approximations: rounding and truncation
- - Mathematical Terminology
- - Proportional Reasoning
- - Number Sense
- - I Don't Get It
- - Percentages
- - Contact the MESH team
- - MESH Research
- - Resources for Staff
- - Smart Assessment Design Toolkit
- - Placements Hub
- - Digital Learning
- - Academic Integrity
- - Academic Integrity Research
- Professional Learning @ Western
- Curriculum Renewal
- The 21C Project
- Contact Us
- Engaged Teaching
Approximations: rounding and truncation
There are many times when computations are done with approximations to numbers, sometimes by choice, sometimes because there is no other way. In this module we look at two ways of approximating numbers: rounding and truncation.
These pages can also be downloaded as a (non interactive) PDF file from here.
Truncation
Truncation is a method of approximating numbers. It is easier than rounding, but does not always give the best approximation to the original number. Truncation is used in computing when division is done with integers and the answer must be an integer.
The number $e$ is $$e=2.718281828459045\dots$$
Sometimes a number is approximated by just ignoring digits. This is called truncation.
Examples
- $e$ truncated to give and integer is $2$;
- $e$ truncated to a number with $1$ decimal place is $2.7$;
- $e$ truncated to a number with $2$ decimal place is $2.71$;
- $e$ truncated to a number with $3$ decimal place is $2.718$;
- $\pi =3.14159\dots$ truncated to give an integer is $3$;
- $-\pi =-3.14159\dots$ truncated to give an integer is $-3$;
- $\pi =3.14159\dots$ truncated to give a number with $3$ decimal places is $3.141$.
Practice questions
Mobile options: