Frustrated Over Sig Figs Calculation

[fiziksfun]

This problem is really making me mad.

I'm supposed to solve it using the correct sig figs

((4.80*10^4)(1/1000) = 48.0

HOW DOES THIS ONLY HAVE THREE SIG FIGS?

doesn't 1000 only have one sig fig and 4.80*10^4 has 5 ?? I'm so confused! HELP!

 

[symbolipoint]

The number shown as 1000 has FOUR significant figures. If it were to be shown as ONE significant figure, it would need to be written as "1 * 10^4" (to the best than may be represented in a purely text-set format).

 

[Hitman2-2]

Well $$4.80 \cdot 10^4$$ actually has 3 significant figures. When you have a number in scientific notation, such as this one, only count the number of sig figs in the factor multiplied by 10ⁿ (which in this case is 4.80).

As for the number 1000, my understanding is that numbers with trailing zeros and no decimal point can be a bit ambiguous. It could have 1, 2, 3, or 4 sig figs. The "1" could be the only significant figure or the "1000" could be written as $$1.0 \cdot 10^3$$ or $$1.00 \cdot 10^3$$ or $$1.000 \cdot 10^3$$. Without seeing the actual problem I can't tell. Sometimes in problems you will convert units, for example, meters to millimeters and you'll have the number 1000 in your calculation. I think that in these cases you don't consider the 1000 in counting sig figs as there is no uncertainty involved (there are exactly 1000 millimeters in 1 meter).