# Thread: Standard Form/Scientific Notation Question.

1. ## Standard Form/Scientific Notation Question.

Hello Everyone, I'm new to the forum. A friend of mine told me how helpful you guys were, and I was wondering if anybody here would answer my question regarding scientific notation.

I've recently been required to revise scientific notation, which is a subject I havn't studied for many years, and that combined with my mathematical ineptness has led to my confusion.

I understand it loosely, but came across a question, the answer to which, has thrown me.

I was asked to calculate the volume of a box, having been given it's length, width and height.

Width = 2.56 x 10 to the power of -6m
Length = 1.4 x 10 to the power of -7m
Height = 2.75 x 10 to the power of -4m

I simply multiplied the digits together to get 9.856 and then multiplied the powers.

I ended up with the answer 9.856x10 to the power of -17 m3

I think that's the correct answer, but doesn't that mean the volume is smaller than each of the length,width and height? Since there's more 0s after the decimal point. How can a volume be smaller? I'm sure I've missed something obvious but I just need a prod in the right direction!

Thanks in advance to anyone who helps!

2. i think you cannot compare length and volume by just looking at their values they two different dimensions. So it's possible to have a situation that you've mentioned

if you really want to compare,

take $\displaystyle 2.56x10^-6$ for example

if it was a volume, it can be taken as $\displaystyle 2.56$x$\displaystyle 10^{-6}$x$\displaystyle 1$ x$\displaystyle 1 m^3$(length=$\displaystyle 2.56x10^6$m, width=$\displaystyle 1$m, height=$\displaystyle 1$m)

so comparing this with your final answer it should obviously less than this one.

but of course since it's not a volume you can't compare a length with a volume..

3. I agree that one cannot compare length and volume as physical magnitudes, though the numerical values, of course, can be compared.

If a number x is multiplied by another number y that is less than 1, then the result is less than x. For instance, 10 * 0.1 = 1 < 10. Similarly, 0.2 * 0.1 = 0.02 < 0.2. Since each of your dimensions is less than 1, the volume is numerically smaller than each of the dimensions.