Op Amp output range

Consider the following scenario:

The supply voltages of op amp (rail to rail) is 5V. Amplification factor of the op amp is 100. Which means if the input is 0.01 volt, the output will be 1V. If the input is 0.02 volt, the output will be 2V.

But if for instance input is 1V math says the output will be 100V. Or if input is 10V, output will be 1000V. But in these two cases output is greater than the supply voltages. Is that possible?

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Nope. The supply voltage is the limit. There's no way the opamp can create a higher voltage than its supply. You mention rail-to-rail, by which you mean the difference between positive and negative supply. But rail-to-rail in opamps also has a different meaning. A rail-to-rail output opamp will have its maximum output close to the positive power supply (minus a few tens of mV) and the minimum output close to $V_-$. If you have a regular opamp the maximum output will be 1.5V to 2V less than $V_+$, so in your case +3V to +3.5V. That's for 1V in. Look up output voltage swing in the datasheet. Note that for a +5V single supply the output range will be limited to something like 2V to 3V, which may be of little use. For such low supply voltages in general a rail-to-rail opamp is used.