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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.
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Is two thirds a rational number?
Yes, two thirds is a rational number. This is because it a is recurring decimal and can be expressed as a fraction. All fractions are rational numbers and all recurring decimals are rational numbers.
Is 5.7 repeating rational?
Yes. Any terminating or non-terminating recurring decimal is a rational number.
Is - 0.29292929292929 a rational number or an irrational number?
Any terminating decimal or repeating decimal is a rational number.-0.29292929292929 iseither a terminating decimal of the fraction -29292929292929/100000000000000or meant to be a recurring decimal (0.2929...) with the '29' recurring forever of the fraction 29/99Either way, it is a rational number.
Is this a rational number 0.323232?
A rational number is a number that can be expressed as the division a/b where a and b are both integers. In this case 0.323232.... is a recurring decimal, and so is rational, as all recurring decimals are rational. This can be proved in the following way: 0.323232... x 100 = 32.323232... 0.323232... x 100 - 0.323232... = 32 0.323232... x 99 = 32 0.323232... = 32/99 Therefore 0.323232... is a rational number.
Is 0.58585858 a rational number or an irrational?
If that is a terminating decimal: 0.58585858 = 58585858/100000000 = 29292929/50000000 And thus a rational number If it's a recurring decimal: 0.58585858... = 58/99 And thus a rational number
