# Measurement - Difficulties

Difficulties

Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time it takes an object to fall a distance of one metre (about 39 in). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of error that arise:

1. This computation used for the acceleration of gravity 9.8 metres per second squared (32 ft/s2). But this measurement is not exact, but only precise to two significant digits.
2. The Earth's gravitational field varies slightly depending on height above sea level and other factors.
3. The computation of .45 seconds involved extracting a square root, a mathematical operation that required rounding off to some number of significant digits, in this case two significant digits.

So far, we have only considered scientific sources of error. In actual practice, dropping an object from a height of a metre stick and using a stopwatch to time its fall, we have other sources of error:

1. Most common, is simple carelessness.
2. Determining the exact time at which the object is released and the exact time it hits the ground. There is also the problem that the measurement of the height and the measurement of the time both involve some error.
3. Air resistance

Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic.