A problem with significant figures

[Richlair]

Homework Statement

The side of a cube is 12.04 cm. Write it's surface area rounded off to the appropriate significant figures.

Homework 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.

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?

 

[Dickfore]

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

 

[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.

 

[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.

 

[rwisz]

As a scientist, it is important to understand the rules for significant figures and how to properly round off numbers. In this case, the side of the cube is given with four significant figures, so the surface area should also be expressed with four significant figures. Therefore, the correct answer is 869.8 cm^2, as given in your book.

Your doubt about rounding to one significant figure is not correct. When multiplying or dividing numbers, the answer should have the same number of significant figures as the number with the least number of significant figures in the calculation. In this case, that number is 12.04, which has four significant figures. Therefore, the answer should also have four significant figures.

It is also important to note that significant figures represent the accuracy of a measurement or calculation, not the precision. In this case, the side of the cube is given to the hundredths place (12.04 cm), so the surface area should also be expressed to the hundredths place (869.8 cm^2). Rounding to the nearest hundred (900 cm^2) would result in a less accurate answer.

In summary, the surface area of the cube should be expressed with four significant figures (869.8 cm^2) to accurately represent the precision of the given measurement.