Rules regarding significant figures:
1) Non-zero digits are always significant.
2) Any zeros between two significant digits are significant.
3) A final zero or trailing zeros in the decimal portion ONLY are significant.
-----------------
Step 1
In subtraction and addition operations:
The final answer may have no more significant figures to the right of the decimal than the LEAST number of significant figures in any number in the problem.
Procedure:
Numerator)
34.123 has 5 significant figures
8.60 has 3 significant figures
Therefore, (34.123 + 8.60) = 42.723 = 42.72 according to this rule
------
Denominator)
98.7654 has 6 significant figures and 5.945 has 4.
Therefore, 98.7654 - 5.945 = 92.8204 = 92.820 according to this rule
------
Division)
The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.
42.72 has 4 significant figures and 82.820 has 5
[tex]\frac{\left(34.123+8.60\right)}{\left(98.7654-5.945\right)}=\frac{42.72}{92.820}=\text{ 0.46024 = 0.4602}[/tex]Answer: 0.4602 (4 significant figures)
