which of the following statements is true
a: positive numbers are always rational numbers
b: negative numbers are always irrational
c: negative numbers are sometimes rational
d: negative numbers are always integers **
idk , found this tough .. but check ?
-2.37 ?
the ** means he thinks that that is the correct answer
To determine which of the statements is true, we need to understand the definitions of rational numbers, irrational numbers, and integers.
1. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers. For example, 1/2, 3/4, and 5/1 are all rational numbers.
2. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They are non-terminating, non-repeating decimal numbers. Examples of irrational numbers include √2 (square root of 2), π (pi), and e (Euler's number).
3. Integers: Integers are whole numbers (both positive and negative) and zero, without any fractions or decimal parts. Examples of integers include -3, -2, -1, 0, 1, 2, 3.
Now, let's evaluate each statement:
a: Positive numbers are always rational numbers.
This statement is false. While some positive numbers can be expressed as a fraction, like 1/2 or 3/4, there are also positive numbers that are irrational, such as √2 or π. Therefore, not all positive numbers are rational.
b: Negative numbers are always irrational.
This statement is also false. While some negative numbers can be irrational, like -√2 or -π, there are also negative numbers that are rational, like -1/2 or -3/4. Therefore, not all negative numbers are irrational.
c: Negative numbers are sometimes rational.
This statement is true. As mentioned before, negative numbers can be rational or irrational. For example, -1/2 is a negative rational number, while -√2 is a negative irrational number.
d: Negative numbers are always integers.
This statement is false. Negative numbers can be integers or non-integers, depending on whether they have a decimal part or not. For example, -3 is a negative integer, while -2.5 is a negative non-integer.
So, the correct answer is c: Negative numbers are sometimes rational.