Is it possible to express every decimal as a fraction (without rounding)? Why or why not?

Yes, you would just have to change the denominator. For example, .2 would be 2/10 and .201 would be 201/1000. A good rule of thumb is to use place value.. ____2____ _____0_____ ______1_____      tenths     hundredths     thousandthsSince the last place value is thousandths my denominator is going to be in the thousands. 

If the decimal ends, then always yes.When you read the decimal, you call it some number oftenths, or hundredths, or thousandths, or millionths etc.,and what you call it when you read it consists of the samewords you use when it's written as a fraction.If the decimal never ends but just keeps going on forever,then ...---  if the same group of digits repeats over and over, (as they do in thedecimal form of 1/3, 1/7, and 1/9), then the decimal can be expressed as a fraction, even though the decimal never ends.--  if a group of digits doesn't repeat, (as in 'pi' or 'e' for example), thenthe decimal is an irrational number  The definition of an irrational numberis one that can't be expressed as a fraction.