The number 0.45 with a two dot on top means a continuous 0.45454545454545...

This is considered rational because it can be expressed as a fraction of two integers.

Let’s say x = 0.45 with a two dot on top, so x = 0.4545454545...

Observe that multiplying x by 100 shifts the decimal two places, so that 100x = 45.45454545...

Even though the 100x appears to be lacking in two digits ‘45’ because the decimal has been shifted, continuous numbers like this never have an end to the decimal, so in this case the digits after the decimal point for both 100x and x are treated to be the same.

100x - x = 45 (since the digits after the decimal are identical and thus they cancel out)
99x = 45
x = 45/99 = 5/11

So 0.45 with two dots on top has the equivalent fraction of 5/11, which is a fraction of two integers 5 and 11, hence 0.45 with two dots on top is a rational number.

You can type in 5/11 on your calculator and observe the digits.