Which of the following is a rational number:
2π, 60, 61−−√, or 0.37815?
Only 0.37815.
The rational number is 60.
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Out of the given options, the number 60 and 0.37815 can be expressed as a quotient of two integers, so they are rational numbers.
However, 2π and √61 are not rational numbers.
Therefore, the rational numbers among the options are 60 and 0.37815.
To determine which of the following numbers is rational, we need to understand what a rational number is.
A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero.
Let's analyze each of the given options:
1. 2π: This is an irrational number since π (pi) is an irrational number, meaning it cannot be expressed as a fraction of two integers.
2. 60: This number is rational since it can be expressed as the fraction 60/1, with both the numerator and denominator being integers.
3. 61−−√: This number is irrational since it involves the square root of a non-perfect square (square root of 61).
4. 0.37815: This number seems to be a decimal, but to determine if it is rational, we need to check if it can be written as a fraction.
To do this, we can convert the decimal into a fraction. The given decimal can be written as 37815/100000, which is a fraction with both an integer numerator and denominator. Therefore, 0.37815 is a rational number.
To summarize, out of the given options, only 60 and 0.37815 are rational numbers.