The Basic Stuff
When you do addition or subtraction, you follow the least d.p for deciding how the final answer should be written. For instance, a = 5.0 (1 d.p) + 7 (zero d.p) = 12 (zero d.p), and not 12.0 (wrong answer).
When you do multiplication or division, you follow the least s.f for deciding how the final answer should be written. For instance, V = 5.0 m then you will get 1/V = 0.20 m-1. At this point, you might be wondering why the answer is not 1 s.f? Why are we not considering the s.f of number 1 in the nominator? The answer to this is simple. That number 1 has infinite number of s.f. Any constant that is part of the formula (e.g 1/2 in KE = ½ mv2) or like 5 books or 14 bricks, when you insert into the calculations, such constant should be treated as having infinite s.f. Thus, you can ignore them since the term with lowest s.f has the most say here!
Computation of angle: 2 d.p in working steps and 1 d.p as your final answer. This is different from computing of numbers where you presented the 5 s.f value before rounding off to required s.f for your final answer. HOWEVER, do note that if you are measuring an angle in your practical, using a protractor, then your angles should be given to whole numbers during recording.
Computation of cost/money: 2 d.p in dollars or whole integer when done in cents.
When taking average, you follow the d.p of the data. For instance, finding the average time taken of t1= 24.5 s and t2= 24.7s. Then t_ave = (24.5 + 24.7)/2 = 24.6 (1 d.p, not 3 s.f)
Find period of a pendulum from average time taken of 20 oscillations. T = t_ave/20. In this case, T follows the s.f of t_ave. Not d.p.
The value of trigonometric function: sin (45 degrees) = 0.707; sin (45.0 degrees) = 0.7071.
Find the acceleration of the block below.