>She is in 5th grade and this is her homework...
>
>So, what if it were 28.5 * 1.843? Then 28 * 1.8? 29 * 2? What are the rules? What is significant?

By the way, sgnificant digits are not only used for quick mental estimations, but also as a quick guideline rounding final results so they don't look more accurate than they actually are.

There is a story about a person who worked in a museum, who claimed that a certain dinosaur skeleton had an age of 70,000,27 years. How could he know the age with such precision? "Well, when I started to work here, they told me it was 70,000,000 years old. That was 27 years ago." This is both funny and exaggerated, but it clearly shows how a precision that is higher than warranted by the actual calculations is absurd. (In this case, one of the numbers was rounded to millions of years, or perhaps to tens of millions - so the final result should also be rounded to millions or tens of millions).

The above paragraph refers to additions and subtractions; in multiplications and divisions, significant digits are often used. If one factor has 3 s.d. and one has 2 s.d., the final result should usually be rounded to 2 s.d.

There are some complex issues involved. Let's start with a few examples:

2.4 has 2 significant digits
2.40 has 3 significant digits
2.408 has 4 significant digits
0.0003 has 1 significant digit
53,000,000 has 2 significant digits

Usually you can assume that zeroes at the end are the result of rounding (although it may not be the case; 53 million may just happen to be closer to 53.0 million than to 53.1 million or to 52.9 million).

After a decimal point, zeroes added at the end - as in 2.40 - are placed there to signify a greater precision. See my first two examples.

Zeroes in between are, of course, also significant digits, since they are not the result of rounding. See my third example.