word Problem

[jw1986]

I need help with the following word problem.
"Gia's ruler is divided into tenths of an inch. What fraction of an inch represents the greatest possible measurement error due to Gia's ruler? Why?

Not only do I need help with the problem, I would like to know what the word "error" is representing.

I think the answer is 10/10, because the inch is divided into tenths and there are 10 tenths in an inch. Please help

Quintin

 

[mmm4444bot]

Precision ...

Hello JW:

The error represents an overage or shortage that exists between the increments on the ruler.

If this ruler measures the length of a line, and the line ends somewhere between two adjacent 1/10ths marks on the ruler, then a more precise length cannot be determined. The value you get is rounded to the nearest tenth of an inch. The "error" is the part that gets dropped when rounding down or added when rounding up.

EG: The length of a line is 17/20ths of an inch long.

Measure this line with the ruler that has 1/10th-inch marks on it.

The end of this line lies between the 8/10ths (16/20) and 9/10ths (18/20) marks on the ruler.

Since we see that the end of the line is much closer to the 9/10ths mark, we round up and call the length of the line 9/10ths of an inch long.

The difference between 17/20 and 9/10 is the error in our final result.

Now consider ... what is the greatest amount of error that we could possibly commit when measuring with this ruler?

Cheers,

~ Mark