I got this book a couple years ago called Physics Demystified

Basically, no measurement of physical quantity can be entirely accurate. So when you measure a quantity and report a figure, you also imply an error in measurement from the number of meaningful digits.

The reason the estimated error is different(has less room for error that is) in the second example is because the equation has more significant digits(1,50 has three significant digits while 1,5 only has two). The first example has an implied uncertainty of 0,1 because you do not know any more decimals than the reported 1,5, while the uncertainty of 1,50 is 0,01.

>>41126
The text is a little misleading.
>Suppose that you measure a quantity, call it q, and get 1.5 x 10^4 units.

The use of "you" can be misunderstood, since it could mean that the result is exact, that the exact result is known by "you" but it was rounded, that the margin of error is known since "you" measured it and so on.

Assume that you used an instrument or an extern laboratory and it gave the result 1.5 x 10^4 units. You know nothing more than this, only this number, nothing more. Since you don't know the actual quantity, you must assume that q was rounded, that is, 1.5 could be an arbitrary number between 1.45 and 1.54999...