To find the product of 12 with each of the given numbers, we will multiply 12 by each option and determine the type of number (rational or irrational) that results.
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Option 1: 4.2974
- Product: \( 12 \times 4.2974 = 51.5688 \) (a rational number)
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Option 2: 2.6307...
- Product: \( 12 \times 2.6307... = 31.5684... \) (since 2.6307... indicates a non-terminating decimal, let's say it continues indefinitely, it will still result in a rational number)
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Option 3: 2.8867
- Product: \( 12 \times 2.8867 = 34.6404 \) (a rational number)
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Option 4: 4.1569...
- Product: \( 12 \times 4.1569... = 49.883... \) (again, this will be a rational number)
Thus, all the computed products turn out to be rational numbers. Therefore, none of the options provided result in an irrational number when multiplied by 12.
Please ensure to double-check the definitions of the numbers provided as typically irrational numbers are non-terminating and non-repeating, while rational numbers can be expressed as a fraction of two integers. In the options provided, it seems like all the products would yield rational results.
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