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### Greatest Possible Error

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Date: 02/11/99 at 23:06:58
From: Brenda
Subject: Greatest possible error

I need an elementary level answer to what is the greatest possible
but I need an answer that students in fourth grade can understand, with
an example. If you could help, that would be great.

Thanks,
Brenda Brouwer
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Date: 02/12/99 at 12:14:42
From: Doctor Peterson
Subject: Re: Greatest possible error

Hi, Brenda. I'll see if I can help.

It would be helpful if you could give me an example to show the context
of your question - what kind of error you have in mind. I assume you
are referring to this answer, which covers several different aspects of
the question:

http://mathforum.org/dr.math/problems/ann4.18.98.html

Suppose you are given a measurement a friend has made - say that the
height of his room's ceiling is 7 feet. In one sense the greatest
possible error is "infinite" - your friend might simply be lying! But
we'll assume that we can trust him, and the height really is 7 feet.
The question is, how far off might he be and still be considered
correct? That depends on how he stated his measurement. He might say,
"It's exactly seven feet, according to precise surveying instruments",
or he might have said "It's about seven feet, as close as I can
estimate without using a ruler." But let's again suppose that he
actually made a measurement, but all he said was "7 feet." What might
the actual height be?

Any number that would round off to 7 feet would be reasonable. If he
measured 7 feet 3 inches, but didn't trust his measurement much, he
might round it off to 7 feet. But if he measured 9 feet, he certainly
couldn't honestly tell you 7. Even if he measured 7 feet 9 inches, he
would have rounded it off to 8 feet. So any number between 6 1/2 and
7 1/2 feet is possible for the actual height. So we would say that the
"maximum error" in the measurement as he expressed it is 1/2 foot.

The hard part is that we don't know for sure how much accuracy he was
trying for. If he told us 80 inches, we wouldn't know whether he
rounded it off to the nearest inch (up to a 1/2-inch error) or to the
nearest 10 inches (up to a 5-inch error). So when accuracy matters, we
try to be more specific about it, and say something like "7 feet to
the nearest inch," or "7 feet plus-or-minus half an inch." That's a lot
more useful than trying to read something into the number we were
given.

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