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Answer :
1) 43.123456789
\(\Rightarrow \) \(43.123456789 = {43123456789 \over {10^9}} = {43123456789 \over {2^9 × 5^9}}\)
The above expression has denominator of the form \(2^n × 5^m\) where n and m are non-negative integers.
So, the number is a rational number, a terminating decimal number.
2) .0.120120012000120000…
Since,the given number is a non terminating non repeating number, it is not rational.
3) 43.123456789123456789....
The number is a rational number because decimal expansion is non terminating repeating.
It has denominator of the form \(2^n × 5^m\) where n and m are non-negative integers.