Math question!? Significant figures.?

Question

Yeah i need help with significant figures. Could someone gimme the rules and stuff. Like when zero's are considered significant and when they're not. If you give examples, that'll help too. Thx.

Answer 1

The first significant figure is the first non-zero digit. Once you indentify this first s.f., all the digits following it are significant.

E.g. Correct 12345 to 2 s.f.

Ans: 12000

E.g. Correct 3.203 to 3 s.f.

Ans: 3.20

E.g. Correct 0.009697 to 2 s.f.

Ans: 0.0097

Answer 2

Non-zero digits are always significant. Thus, 22 has two significant digits, and 22.3 has three significant digits.

With zeroes, the situation is more complicated:

Zeroes placed before other digits are not significant; 0.046 has two significant digits.

Zeroes placed between other digits are always significant; 4009 kg has four significant digits.

Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.

Zeroes at the end of a number are significant only if they are behind a decimal point as in (c). Otherwise, it is impossible to tell if they are significant. For example, in the number 8200, it is not clear if the zeroes are significant or not. The number of significant digits in 8200 is at least two, but could be three or four. To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point:

8.200 x 10 to the 3rd has four significant digits

8.20 x 10 to the 3rd  has three significant digits

8.2 x 10 to the 3 has two significant digits