How to Calculate Greatest Possible Error

Date: 04/12/2004 at 18:08:29
From: Richelle
Subject: Help! Greatest Possible Error, Don't understand

I'm an 8th grade student working on greatest possible error and it
just doesn't seem to make any sense.  I know that GPE is half of the
smallest unit of measure, but what I don't understand is how does one
find half of the smallest unit of measure?

For example, what is the GPE of 8 ft?  When it says to take half of
the smallest unit of measure my mind says to divide 8 ft by 2.  What
am I doing wrong?

Date: 04/12/2004 at 21:30:59
From: Doctor Achilles
Subject: Re: Help! Greatest Possible Error, Don't understand


Hi Richelle,

Thanks for writing to Dr. Math.

That's a good question.  GPE is sort of like the reverse of rounding.

For example, let's say I tell you that I am about 6 ft tall.  What 
range would you guess my height is?  Well, if I were really 5.3 feet 
tall, then saying that I'm about 6 ft tall would be a lie.  If I'm 5.3 
feet tall, it would be more honest to call myself "about 5 feet tall".

What if I'm really 5.7 feet tall?  Then it's probably ok to tell you 
I'm "about 6 feet tall" since I'm closer to 6 feet than I am to 5 
feet.

So what range of height can I have for it to be ok for me to tell you 
that I'm "about 6 feet tall"?  Anywhere between 5.5 and 6.5 feet tall 
is fine.  So if I tell you I'm 6 feet tall, then that really means 6 
feet plus or minus 0.5 feet.  So the GPE for "6 feet" is 0.5 feet, or
half a foot.

Let's say that instead I tell you that I'm "5 feet, 9 inches tall".  
What is the GPE?  Well, if I'm less than 5 ft, 8.5 inches tall, then I 
should've told you that I was 5 ft, 8 in.  And if I'm more than 5 ft, 
9.5 inches tall, then I should've told you I was 5 ft, 10 in.  So that 
means that I am somewhere between 5 ft, 8.5 in and 5 ft, 9.5 in.  So
the greatest possible error from my 5 ft, 9 in estimate is 0.5 inches,
or half an inch.

What if I told you that I am "5 feet, 8.7 inches tall".  Well, in 
order for that to be true, I had better be more than 5 ft, 8.65 in and 
less than 5 ft, 8.75 in.  So the GPE for 5 ft, 8.7 in is 0.05 inches,
which is 5/100 or 1/20 of an inch.

So to find GPE, you take the most precise unit and divide that unit 
by 2.  You can also think of dividing by two as multiplying by 1/2 if
that's easier to understand.

So when the most precise unit is feet, the GPE is 0.5 feet.

When the most precise unit is inches, the GPE is 0.5 inches.

When the most precise unit is tenths of inches, the GPE is 0.05 
inches.

Does that make sense?

Hope this helps.  If you have other questions or you'd like to talk 
about this some more, please write back.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 04/12/2004 at 22:16:11
From: Richelle
Subject: Thank you (Help! Greatest Possible Error, Don't understand)

Thank you so much for helping me.  I get it now.