significant figures

Question

would number of years be an exact number? For example, a question asks how many minutes in 3.5 years? I got 1839600 minutes but i dont know how i should round for sigfigs. is it to 2 sig figs or is 3.5 years an exact number so there is an unlimited number of sigfigs?

Answer 1

Number of years is not an exact number. The amount of years could be more exact in your problem -- you could be given 3.52 years for example.

Think about this in everyday speech: If someone told you that they've been at their job for 3 and a half years, you would not think they meant exactly 3.5 years down to the minute, second, and fraction of a second.

Exact numbers come in two categories (off the top of my head)

1. Counting numbers -- if you have three objects and you want to take the average mass of them say, you have exactly three. You would add up the masses and then divide by 3. But the 3 in your calculation would not determine the number of significant figures -- your measurements of mass would.
2. Conversion numbers (where the conversions are definitional). For instance, 1 kg is exactly 1000 grams by definition. So if your calculation involved a conversion, you wouldn't say that 1000 has 4 significant figures and use that to round your final answer. In your problem, there are 60 minutes in an hour and 24 hours in a day, etc. so these are all exact numbers.

In your problem, 3.5 years has 2 significant figures, so your answer should be rounded to 2 significant figures.