Which of the following is a rational number :2π, 6/6, 61−−√, or 0.37815
The rational number of the options given is 6/6.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers and the denominator is not zero.
Looking at the options:
1. 2π is an irrational number since it cannot be expressed as a fraction.
2. 6/6 is a rational number because it can be simplified to 1, which is a whole number.
3. 61−−√ is an irrational number since it involves the square root of a non-perfect square.
4. 0.37815 is a rational number since it can be expressed as a fraction. However, to verify this, we need to check if it can be written as a fraction in the form a/b, where a and b are both integers with b not equal to zero.
To convert 0.37815 to a fraction, we can determine the fraction's decimal representation. By multiplying both the numerator and denominator by 100, we can move the decimal point two places to the right:
0.37815 * 100/100 = 37.815/100
Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:
(37.815/5) / (100/5) = 7.563/20
Thus, 0.37815 is a rational number since it can be expressed as the fraction 7.563/20.
In summary, the rational numbers among the given options are 6/6 and 0.37815.