Sure, let's determine which of the given numbers are rational, because rational numbers can be expressed as a fraction of two integers, where the denominator is not zero.
1. [tex]\(-19\)[/tex]
- A rational number can be an integer. Since [tex]\(-19\)[/tex] can be expressed as [tex]\(\frac{-19}{1}\)[/tex], it is a rational number.
2. [tex]\(-\frac{2}{5}\)[/tex]
- This is a fraction where both the numerator ([tex]\(-2\)[/tex]) and the denominator (5) are integers, and the denominator is not zero, so [tex]\(-\frac{2}{5}\)[/tex] is a rational number.
3. 0
- Zero is an integer and can be written as [tex]\(\frac{0}{1}\)[/tex]. Hence, 0 is a rational number.
4. [tex]\(\frac{4}{7}\)[/tex]
- This is a fraction where both the numerator (4) and the denominator (7) are integers and the denominator is not zero, so [tex]\(\frac{4}{7}\)[/tex] is a rational number.
5. 1.091502
- This is a decimal number. Since it can be written as [tex]\( \frac{1091502}{1000000} \)[/tex] (where both 1091502 and 1000000 are integers), it is a rational number.
6. 2.89
- This is a decimal number. Since it can be written as [tex]\(\frac{289}{100}\)[/tex] (where both 289 and 100 are integers), it is a rational number.
To summarize, all the numbers provided are rational numbers.
Therefore, the numbers which are rational are:
[tex]\(-19\)[/tex]
[tex]\(-\frac{2}{5}\)[/tex]
0
[tex]\(\frac{4}{7}\)[/tex]
1.091502
2.89
