How do you round numbers to 3 significant figures?

Answer 1

There are three rules that are used when rounding to a desired number of significant digits (figures):

1. All digits that are not zero, are significant

2. In a number that does not have a decimal point, all zeros between two non-zero digits are significant digits

3. In a number that has a decimal point, all zeros after the leftmost non-zero digit are significant

Examples:

12345 rounded to 3 significant digits: 12300, or 1.23 x 104

12.345 rounded to 3 significant digits: 12.3, or 1.23 x 101

0.012345 rounded to 3 significant digits: 0.0123, or 1.23 x 10-2

0.012045 rounded to 3 significant digits: 0.0120, or 1.20 x 10-2

In the last example the zero after 2 is significant. That is the reason for keeping it in the result when rewriting it in powers of 10 notation.