# Thread: Significant figures and exponential notation

1. ## Significant figures and exponential notation

I've always been confused by how to determine the number of significant figures when the expressions involve both two types of operations and exponential notation. I've been through several introductory physics/chemistry courses and still don't know how to do this. I've asked the professors and heard other people ask the exact same question but only received a reply which sounded like they didn't know what I was asking. Anyway, it's really getting on my nerves, so could someone please work out for me exactly what you would do to solve questions like the following two? I think that will be much easier than me trying to explain the questions I have.

1. 320.55 - (6104.5/2.3)
2. [(285.3 * 10^5) - (1.200 * 10^3)] * 2.8954

For example, for the first question I first divide 6104.5 by 2.3, getting 2654.13043, which is rounded to 2.6 * 10^3 because it can only have two significant figures. But how do you calculate decimal places (to figure out how many significant figures the difference should have) when you are expressing one of the addends in exponential notation? Even if that issue is resolved, i am not sure how to express the answer. I hope I've explained myself clearly and am not making a stupid mistake.

2. Originally Posted by Dana_Scully
I've always been confused by how to determine the number of significant figures when the expressions involve both two types of operations and exponential notation. I've been through several introductory physics/chemistry courses and still don't know how to do this. I've asked the professors and heard other people ask the exact same question but only received a reply which sounded like they didn't know what I was asking. Anyway, it's really getting on my nerves, so could someone please work out for me exactly what you would do to solve questions like the following two? I think that will be much easier than me trying to explain the questions I have.

1. 320.55 - (6104.5/2.3)
2. [(285.3 * 10^5) - (1.200 * 10^3)] * 2.8954

For example, for the first question I first divide 6104.5 by 2.3, getting 2654.13043, which is rounded to 2.6 * 10^3 because it can only have two significant figures. But how do you calculate decimal places (to figure out how many significant figures the difference should have) when you are expressing one of the addends in exponential notation? Even if that issue is resolved, i am not sure how to express the answer. I hope I've explained myself clearly and am not making a stupid mistake.
It is best to always write "significant figures" in exponentials- that way you know if a 0 is "significant" or not. For example, "6*10^5" has one significant figure while "6.0*10^5" has two significant figures and "6.00*10^5" has three. Those would all be written as 600000 in "regular" notation but the number of significant figures is ambiguous.

In (2), above, you would recognize that both 285.3 * 10^5 and 1.200 * 10^3 have 4 significant figures. To subract them you will need to write them as 28430000 and 1200 or at least 28530 *10^3 and 1.200 * 10^3 so that the differencce is 29428800 or 29428.8*10^3. Since our original numbers had 4 significant figures, both of those would be written 2.943*10^7. Now multiplying that by 2.8954, which is 2.895 to four significant figures, we get 8.520*10^7.