Which of the following is a rational number: 2π, 60, 61−−√, or 0.37815?(1 point)
Which of these is a rational number: 2π, 60, 61−−√, or 0.37815?(1 point)
Which of the following is an irrational number: −1529, 0.343434..., 2√3, or 87.9821?(1 point)
Which of the following is a rational number: 2π, 6/0, 61−−√, or 0.37815?(1 point)
To determine which of the following is a rational number, let's review what a rational number is. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero.
Now let's analyze each option:
1. 2π: This is not a rational number. π is an irrational number (approximately 3.14159...) and cannot be expressed as a ratio of two integers.
2. 60: This is a rational number. It can be expressed as the ratio 60/1.
3. 61−−√: This is not a rational number. The presence of the square root (√) symbol indicates that it is an irrational number.
4. 0.37815: This is not a rational number. It is a decimal representation, but it cannot be expressed as a ratio of two integers.
Therefore, the only rational number among the options is 60.
To determine which of the given numbers is a rational number, we need to understand what a rational number is.
A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. In other words, a rational number can be written as a fraction in the form a/b, where 'a' and 'b' are integers and b is not equal to zero.
Let's analyze the given options:
1. 2π: This number is an irrational number because π (pi) is an irrational number, meaning it cannot be expressed as a fraction or a ratio of two integers.
2. 60: This number is a rational number because it can be expressed as the fraction 60/1, and both 60 and 1 are integers.
3. 61−−√: This number is an irrational number because the square root of 61 cannot be expressed as a fraction or a ratio of two integers.
4. 0.37815: This number is a rational number because it can be expressed as a fraction by writing it as 37815/100000, which can be simplified further if needed.
Therefore, the rational number among the given options is 60.