If a train travels 891 km from Berlin to Paris and then overshoots the end of the track by 13 m, (a) what is the percentage error in the total distance covered? (b) Is it correct to write the total distance covered by the train as 891013 m? Explain.

Solution: If a train travels 891 km from Berlin to Paris and then overshoots the end of the track by 13 m, (a) what is the percentage error in the total distance covered? (b) Is it correct to write the total di

If a train travels 891 km from Berlin to Paris and then overshoots the end of the track by 13 m, (a) what is the percentage error in the total distance covered? (b) Is it correct to write the total distance covered by the train as 891013 m? Explain.

For any problem that involves error, the formula we'll use is

$\%error=\frac{(measurement-acceptedvalue)}{acceptedvalue}\times 100\%$

An "accepted value" in science is a measurement that's been repeated many times and accepted as accurate. The "measurement" is a value from a single experiment.

**(a)** For this problem, the 891 km the train is *supposed* to travel is the *accepted value*. We're told it overshoots the end of the track by 13 m, so

$(measurement-acceptedvalue)=13\mathrm{m}$