How can you control the number of significant figures in a number that ends in what should be significant 0's

Question

Here's an example... Lets say you measured the distance from Earth to some random star, and found it to be 12,000,000,000 light years away, accurate to the nearest light year, now since you measured that distance with your super 1-light-year-long measuring sticks (lol), you know your answer is accurate to the nearest light year... So the 9 zeros at the end of the number SHOULD be considered significant, but by following the rules for significant figures, you only assume the 1 and 2 to be...

How can you signify the significance of those zeros? I know you could do it like this...
1.2000000000*10^10
But is that how you should always do it? Or is there another way?

Thanks.

P.S. I classified this under chemistry because you seem to use the concept the MOST there, I understand you use it in other fields, and probably least of all in mathematics ( I didn't say not at all), so don't whine about my classification and ask me to put it there... ya...

^Sorry about that part, but ut was needed.

it* (last sentence)

"The other way to express significance is by stating the error in a measurement. For example 12,000,000,000 +/- 5 light years would express the significance more accurrately than just counting digits."

You mean .5 right? I thought of that one but I don't know if anybody uses it, although it is a very easy method to use, jsut make the uncertainty half your measuring unit.

Answer 1

The other way to express significance is by stating the error in a measurement. For example 12,000,000,000 +/- 5 light years would express the significance more accurrately than just counting digits.

Answer 2

i think your bit confused and misunderstanding significant figures,, if we measured any amount with certain device we should write down all the numbers we got from our device,, its give the accuracy of our measurement,, so significant figures is the actual figures and in your example we have 11 Significant Figures. and all these figures can be read on the device and represent measured values

Answer 3

Significant figures include zeros. If you did not express them, you have no idea what they may be. By specifying zeros, you are restricting the uncertainty of the value

Answer 4

You are right, this is the correct way to write this number.

Ana