# A problem with significant figures

1. Jun 26, 2011

### Richlair

1. The problem statement, all variables and given/known data
The side of a cube is 12.04 cm. Write it's surface area rounded off to the appropriate significant figures.

2. Relevant equations
Surface area=6 x side^2
For multiplying, the answer should be written with the number of significant figures equal to the least number of significant available in the numbers in the product.

3. The attempt at a solution
Upon multiplying, the actual answer is 869.7696. In my book, it was given that since 12.04 has four significant figures, we must round off 869.7696 to four significant figures and hence, the answer is 869.8.

My doubt is that, since there is a 6 present in the product that has only one significant number, the answer should be expressed with only one significant number and so, the answer should be 900. Am I right in saying that?

2. Jun 26, 2011

### Dickfore

The 6 in the formula is exact and should be treated like a mathematical constant known to infinite significant figures.

3. Jun 26, 2011

### Fewmet

Dickfore is correct. The same applies to the 2 in the s2 that you used to find the area and the half in A=$\frac{1}{2}$bh.

4. Jun 26, 2011

### AJKing

The question has already been answered, but I thought I'd just throw down one more point.

How many sides of a cube are there?
6.
That's easy.

But, we could be even more precise and say that there are 6.000000000000000000 sides. Since we know the exact value here, it's irrelevant how many digits there are. We normally just use as many significant figures as necessary.