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Error intervals

Error intervals

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Summary

Error intervals

​​In a nutshell

Rounding errors involves looking at a rounded measurement and finding the interval within which the measurement could lie. The range of numbers is called the error interval. An error interval can be found from rounded numbers or truncated numbers. A truncated number is a number where the digits after a certain decimal place have been removed.



Rounded measurements

To find an error interval, look at how the number has been rounded, and think about what range of numbers would round to the rounded answer.

Procedure

1. 

Half the unit that the number is rounded to.

2.

Add this to the number to find the highest value for the rounded number and subtract this number to find the lowest value for the rounded number.

3.

Write the answer as an error interval using inequality notation.


The inequality is written as (lower bound) x<\leq x \lt ​ (upper bound).


Example 1

A pen has a length, xx, of 14cm14cm to the nearest 1cm1cm. Find the error interval for the length of the pen.


Half the unit 1cm1cm.

1÷2=0.51 \div 2 = 0.5​​


Add and subtract this number from 14cm14cm

140.5=13.5cm14+0.5=14.5cm14-0.5 = 13.5cm \\14 + 0.5 = 14.5cm​​​


Write the answer using inequality notation

The error interval is 13.5x<14.5\underline{13.5\le x < 14.5}.


Truncated measurements

Truncation is removing all digits past a certain decimal point. It is like always rounding down. It is possible to find the error interval for truncated measurements.


Example 2

The mass of an object, mm​, is truncated to 5.6g5.6g correct to 11  decimal place. Find the error interval for the mass of the object.


The object could have a mass ranging from 5.6g5.6g up to, but not including, 5.7g5.7g. The error interval is given as


The mass of the object lies in the interval 5.6m<5.7\underline{5.6 \le m \lt 5.7}.


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Exercises

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FAQs - Frequently Asked Questions

How do you display an error interval?

What is a truncated number?

What are rounding errors?

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