Can exact numbers be written in scientific notation I've learned in scientific notation you have last number as probable. Meaning it could be anything...
so in $3$ significant digit number such as follows
$3.34$ has '$4$' which could be anything.
Now if had exact number and I wrote in scientific notation won't that make it inexact as it's implied that in scientific notation last digit is probably something else. 


*

*Exact number: $2650$

*In s. Notation: $2.650$ x $10^3$


So now $0$ is probable and unsure number..?
 A: Certainly I can write $10!=3,628,800=3.6288\cdot10^6$.  This is exact, but if you just see $3.6288\cdot10^6$ you might wonder if it had been rounded.  It may be more useful to write it this way, as it is more evident the magnitude of the number.  There is nothing special about scientific notation.  When you see $\pi \approx 3.1416$ it has been rounded and there is no power of $10$.
A: Muhammad,
What you are missing here is a deeper understanding of significant digits. The general rule of sig. figs. is that the first number of the error (i.e. sigma / standard deviation) is the last significant digit of the measurement. This is were your idea of the last digit being "probable" comes into play.
For example, if you were measuring an unknown sample of 2-pentanone using a calibration curve and got a concentration of 0.71141 with standard deviation 0.0217... The concentration you would report would be 0.71 ± 0.02 Molar using the general rule of sig figs. The last number, "1" from 0.71 is probable because of the error.
Exact numbers are thought of to have an infinite number of sig figs. For example, the number of seconds in a minute (i.e. 60 seconds = 1 minute) or number of inches in a foot (i.e. 12 inches = 1 foot) do not have an error associated with it and so you can report them in scientific notation without losing information.
A: Yes, exact numbers can absolutely be written in scientific notation. It's important to note the difference between scientific notation and the convention of significant figures.
Scientific notation is a standard used to simplify the expression of extremely large and extremely small numbers by expressing the figure as a product with $10^p$. Scientists routinely deal with numbers on both ends of the spectrum, and it's much easier to understand the numbers when they're expressed in this manner. 
If we calculate $4 \cdot 10^6$, our product is always $4,000,000$. It doesn't become $3,000,000$ or $5,000,000$ simply because we expressed the value as a product.
$$ 4 \text{ million}= 4,000,000 = 4 \cdot 10^6 = 4.0 \cdot 10^6 = 4.00 \cdot 10^6 = \ ...$$
Since all of the expressions above equal the same thing, you don't have any loss of accuracy, mathematically speaking.
The concept of significant figures is part of a convention that allow any scientist in the world to immediately understand data that was measured by someone else. Significant figures are not mathematical law. This is why it's likely you were not introduced to this concept in a traditional math course, but rather in a science course.
The convention of significant figures in reporting measurements doesn't change the actual value of the number, it just confers information to anyone interpreting the data that there is a limit to which you believe this figure to be a wholly accurate representation of the quantity of unit being measured. 
In the international scientific community, exact numbers are considered to have an unlimited number of significant figures. Exact numbers can come from only three sources:


*

*Exact counting of discrete objects

*Defined quantities

*Numbers that are part of an equation


Convention for reporting scientific data dictates that the last digit of a reported measurement is the only estimated digit. But this doesn't only apply to values expressed in scientific notation. A reported measurement of $3.54 g$ of sodium chloride indicates the reporting scientist is absolutely certain of the digits '$3$' and '$5$', but the digit in the hundredths place is estimated. This doesn't change if the figure is expressed in scientific notation, where it would be represented as $3.54 \cdot 10^0g$.
This convention ensures that anyone analyzing your data — or you, analyzing someone else's data — will be aware of the degree of accuracy to which their measurements were taken. This is the meaning of "significant figures" in a measurement.
The example you provided is not enough to determine accuracy because we do not know what you are quantifying with your numbers or how you got your measurement. What you're addressing are two separate things. Any number can be expressed in scientific notation.
The idea is that human means of measuring things vary by method of measurement and the unit being measured. We can easily measure the number of pennies sitting in a bowl simply by counting. If I see 10 pennies, I can definitively say there are 10 pennies in the bowl with 100 percent accuracy, which is why the measurement would have infinite significant figures. But I can only estimate the number of atoms in the pennies, because I am limited by the accuracy of the instruments I am using to acquire my measurement.
See these resources for more information:
http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/
http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html
http://en.wikipedia.org/wiki/Scientific_notation#Significant_figures
A: I would regard 3.34 as a three-significant-digit approximation to any number between (exact) 3.335 and 3.345, but not to, for example, 3.37.  So I think "it could be anything" is misleading.
