The number 0.123123123123 is:A. RationalB. TranscendentalC. SurdD. Irrationa
Question
The number 0.123123123123 is:A. RationalB. TranscendentalC. SurdD. Irrationa
Solution
The number 0.123123123123 is a rational number.
Here's why:
A. Rational: A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since 0.123123123123 is a repeating decimal, it can be expressed as a fraction, thus it is a rational number.
B. Transcendental: A transcendental number is a number that is not a root of any non-zero polynomial equation with integer coefficients. The most famous transcendental numbers are π and e. But 0.123123123123 is not a transcendental number.
C. Surd: A surd is a number that can't be simplified to remove a square root (or cube root etc). Examples: √2, √3, √5 etc. But 0.123123123123 is not a surd.
D. Irrational: An irrational number is a number that cannot be expressed as a ratio of two integers. But 0.123123123123 can be expressed as a ratio of two integers, so it's not an irrational number.
So, the answer is A. Rational.
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