Understanding Significant Figures in Physics: Why Only 2 Sig. Figs. for t?

[e-zero]

I have the following info for a question:

x0 = 380m
a = -9.80m/s^2
t = ?
v0 = 0

I use the formula x = x0 +v0t + (1/2)at^2

When I solve for 't' I get 8.80631

I figure I would round to 3 sig. figs. and have t = 8.81s, but my book is telling me t = 8.8 which is only 2 sig. figs.

Why are they reporting only 2 sig. figs. for this question?

 

[Borek]

I agree 8.81s looks better. Apparently authors of the book were not treating significant figures too religiously. Please remember they are only an approximated way of dealing with precision, and not a very good one.

 

[e-zero]

Here is the full question in case I missed something:

Estimate how long it took King Kong to fall straight down from the top of the Empire State Building (380m high).

I assume a = -9.80m^2. The only other thing I see is that the height of the building can be seen as only 2 sig. figs. since the last digit is '0', but I would normally take that as 3 sig. figs. since it is not stated as 'approximate'.

Any input?

 

[Borek]

You haven't missed anything.

 

[pbuk]

In questions involving the acceleration due to gravity at the Earth's surface the key word "Estimate" usually means "assume a = 10 ms^-2". So an estimate would be the square root of 76, or 8.7.

8.81 would be more appropriate if the question said "Calculate..."

 

[the_wolfman]

There is an ambiguity when dealing with significant figures and different people/textbooks use different conventions.

Often 380m indicates two significant figures.
Including a decimal point after the last digit (380.m) would indicate three.

Using scientific notation removes the ambiguity
3.8 is 2 sig figs
3.80 is 3
3.8000 is 5

Many of the introductory physics books I've seen use this convention.

 

[jbriggs444]

I'm impressed. The standard acceleration of gravity is 9.81 m/sec to three sig figs. But the acceleration of gravity in New York city is 9.80 m/sec to three sig figs. You quoted the right value of g.

If King Kong had fallen 380 meters in Jakarta, your result would have been good to only two sig figs.

http://en.wikipedia.org/wiki/Gravit..._gravities_in_various_cities_around_the_world