Two bad principles that taste worse together: Decimals are the true numbers. Rounding makes no difference.
Since students learn about decimals after they've learned about whole numbers and fractions, they might assume that decimals are always the preferred way to represent real numbers, and so everything should be converted to decimals. Meanwhile, since in generally one cannot be expected to write out an infinite decimal expansion, they might assume that stopping after two decimal places makes no difference.
I'm not saying that approximations are bad. But it's bad to approximate if you have no sense of your error tolerance, or even of the fact that you're introducing an error at all.
Here are two perverse outcomes.
- Imagine a problem whose answer is, say, $\pi/4$, and a solution that ends like this: $$\text{blah blah blah} = \pi/4 = 3.14/4 = .785.$$ I'm sure that there are some situations where it's important to know that your answer is between $.78$ and $.79$. But much of the time, conversion to decimals obscures what's going on.
- (Small sample size alert!) About half of my calculus students will, on the first day of class, mark the equation $\frac{1}{3} = 0.33$ as ``true''.