My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

LinkBack Thread Tools Display Modes
October 29th, 2017, 08:42 AM   #1
Joined: Oct 2017
From: London

Posts: 1
Thanks: 0

Maximum absolute error when calculating a difference using two rounded down values.

I have a maths question from an old text book where I disagree with the answer given.
You have 2 pins. One is measured as 12mm and the other is 14mm.
The values measured are rounded down to the nearest mm.
That means the true length of each pin "l1" and "l2" by my calculation would be:-

12 <= l1 < 13
14 <= l2 < 15

That means the actual error for each pin is:-

-1 < E1 <= 0
-1 < E2 <= 0

That means that the maximum absloute error for each pin is just under 1mm.

My problem is what is the maximum absolute error when calculating the difference between the two pins?
Using the given values: 14mm - 12mm = 2mm.

The largest l1 can be is just under 13mm and the lowest l2 can be is 14mm giving a difference of 14mm - 13mm = 1mm.

The lowest l1 can be is 12mm and the largest l2 can be is 15mm giving a difference of 15mm - 12mm = 3mm.

Therefore I calculate the true difference as:-

1 < (l2-l1) < 3

That means the actual error when calculating the difference is:-

-1 < E3 < 1

And so the maximum absolute error in calculating the difference is just under 1mm.

I believe the book says that maximum absolute error in calculating the difference should be just under 2mm (combining the two errors of each measurement) but I can't find a way to combine the errors in this case.

Anyway I needed to check if I was right or if there was something I'm missing before moving on. Thank you in advance for any replies.
trampolinerist is offline  
October 29th, 2017, 06:16 PM   #2
Senior Member
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 551

Asked and answered at FMH
JeffM1 is offline  

  My Math Forum > High School Math Forum > Algebra

absolute, calculating, difference, error, maximum, rounded, values

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Difference Between Maximum/Minimum Value and Maximum/Minimum Turning Point Monox D. I-Fly Pre-Calculus 4 October 13th, 2014 05:58 AM
Find the absolute minimum and absolute maximum. corleoneee Calculus 5 October 22nd, 2013 12:31 AM
Absolute Value Inequality with Absolute Values on Both Sides shiseonji Algebra 2 September 24th, 2013 08:36 AM
Absolute Maximum value calebh Calculus 3 October 21st, 2012 07:42 PM
Calculating Eigen Values error Singularity Linear Algebra 2 April 18th, 2010 01:49 PM

Copyright © 2019 My Math Forum. All rights reserved.