What exactly is loss of precision? Can anyone give an example?

Question

I know it involves the loss of decimal point values, but what exactly is it? Please can someone help... Thanks in advance!

Answer 1

Loss of precision occurs because most numbers can't be represented exactly on a calculator or in a computer. Suppose your calculator can store around 12 decimal digits of a number, and suppose you enter
10286354.8495 - 10286354.8307.
You would expect the answer to be 0.0188 exactly, but it is likely to be something like 0.0188163782436, because the binary representation of the original numbers gave garbage past the twelfth decimal place. So from figures accurate to 12 significant figures, we have gone to a result accurate to only three significant figures.

Answer 2

the loss in precision deals mainly with losses in measurements. even calculations have the purpose of 'to measure' and you are right on the money when you mentioned 'the difference in decimal points'.

in calibration, loss of precision are incurred from different errors. one example is what we call 'paralax error'. this is the error caused by the angle of eyesight to the mesuring devices in subject.

in calculations it is mostly observable on conversions. for example, converting Psi to Mpa, or simply converting fahreinheit to celsius.

in engineering, since errors or precision loss is somewhat viewed as normal or common, you will often hear phrases like 'safety factor' or 'factor of error'.
this denotes that absolute or precise is really hard to attain.

Answer 3

When scientists create reports, they include the quantity they measured as well as the precision used.

More significant figures indicate that the quantity was more precisely measured. Signficant figures must be used in all calculations.