some decimal numbers with fractional part that can be written down easily in base 10 cannot be in base 2 without using infinite series of number(0.2)

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i am not an expert in maths so pardon me for my insufficiency in math vocabulary but noticed a behavior and was curious to know more about it. some numbers like 0.2 can be written easily in base 10 but not so as in base 2 without going till infinity. do such patters emerge when only on the increasing side of base or decreasing also, is this pattern specific to this case or every such of its kind? hypothetically expanding can such bases exist in which even irrational numbers could be depicted?