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Earn +20 ptsQ: Is 3.09 a rational number
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Why is a recurring number rational?
A recurring decimal can always be converted to a fraction with integer numerator and denominator, and that is precisely the definition of a rational number. Example: let the recurring number be 0.3121212... Call the number "x" 100x = 31.21212... x = 0.31212... Subtract the two equations: 99x = 30.9 990x = 309 x = 309/990 This can be simplified, but the point is that I converted the recurring decimal to a fraction, with integer numerator and denominator.
Is the product of a rational number and a rational number a rational number?
yes
Is a rational number multiplied a rational number rational?
Yes.
Is the number 17.5 a rational number?
yes
Which number can be multiplied to a rational number to explain that the product of two rational numbers is rational?
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
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