If you mean 4/9 as a fraction then it is a rational number
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0.444444444 is a fraction. It is a fraction in decimal form rather than in the form of a ratio. However, that does not stop it being a fraction. Its equivalent, in rational form, is 444444444/1000000000. You can simplify this rational fraction if you so wish.
Yes - any proper fraction x/y is a rational number. Expressed as a decimal, this is equal to 0.4 recurring (that is, 0.44444...)
Yes. Any rational number divided by another rational number is also rational.
Yes it is a rational number because it can be expressed as 10/9 as an improper fraction
-0.04 is a fraction. It is a fraction in decimal form rather than in the form of a ratio. However, that does not stop it being a fraction. Its equivalent, in rational form, is -4/100. You can simplify this rational fraction if you require.