Techniques of division by numbers in base n

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Our current number system is in base 10, so we have devised techniques when a number is divided by a power of 10. For example: $\dfrac{350}{100} = 3.5$, by moving the decimal by two places because 100 has two zeros.

If we do division with numbers in base 2, or in any other base, would there be similar techniques? $\dfrac{1010}{10}$?

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Yes, it's the same thing!

For instance, in base $2$, we have

$$\frac{1010}{100} = 10.1$$

This happens because the denominator is really $2^2$, while the numerator is $2^3+2^1$, and in base $10$, we have

$$\frac{2^3+2^1}{2^2} = 2^{3-2} + 2^{1-2} = 2^1 + 2^{-1} = 2.5,$$ which translates to $10.1$ in base $2$.