The number that produces an irrational number when multiplied by 0.4 is 3π. The correct option is A. [tex]3\pi[/tex]
To determine which number produces an irrational number when multiplied by 0.4
First and foremost, 0.4 is a rational number.
A rational number is a number that is of the form [tex]\frac{p}{q}[/tex] where p and q are integers and q is not equal to 0.
0.4 can be written as [tex]\frac{4}{10}[/tex] or [tex]\frac{2}{5}[/tex], hence, it is a rational number.
Now,
Any irrational number when multiplied by a rational number other than zero will also be irrational.
Therefore, we are to determine which of the given options is an irrational number.
π is an irrational number, therefore 3π is also an irrational number
0.444... can be expressed as 4/9, therefore it is a rational number
- For option C. [tex]\sqrt{9}[/tex]
[tex]\sqrt{9}[/tex] = 3, which can be expressed as 3/1, therefore it is a rational number
- For option D. [tex]\frac{2}{7}[/tex]
[tex]\frac{2}{7}[/tex] is a rational number
The only irrational number among the given options is 3π
Hence, the number that produces an irrational number when multiplied by 0.4 is 3π. The correct option is A. [tex]3\pi[/tex]
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