Let’s compare the given rational numbers step-by-step to determine which statements are true.
### Statement i: [tex]\(-4.3 < -3.7\)[/tex]
When comparing negative numbers, the number with the smaller absolute value is actually the larger number because it is closer to zero. Here:
- [tex]\(-4.3\)[/tex] is more negative (farther from zero) than [tex]\(-3.7\)[/tex].
Therefore, [tex]\(-4.3 < -3.7\)[/tex]. This statement is true.
### Statement ii: [tex]\(-3.7 < -2.6\)[/tex]
Similarly, comparing [tex]\(-3.7\)[/tex] and [tex]\(-2.6\)[/tex]:
- [tex]\(-2.6\)[/tex] is closer to zero and thus less negative than [tex]\(-3.7\)[/tex].
Therefore, [tex]\(-3.7 < -2.6\)[/tex]. This statement is true.
### Statement iii: [tex]\(-4.3 > -2.6\)[/tex]
For [tex]\(-4.3\)[/tex] and [tex]\(-2.6\)[/tex]:
- [tex]\(-2.6\)[/tex] is closer to zero and thus less negative than [tex]\(-4.3\)[/tex].
Therefore, [tex]\(-4.3 > -2.6\)[/tex] is incorrect because [tex]\(-4.3\)[/tex] is more negative. This statement is false.
### Statement iv: [tex]\(-1.8 > -0.9\)[/tex]
For [tex]\(-1.8\)[/tex] and [tex]\(-0.9\)[/tex]:
- [tex]\(-0.9\)[/tex] is closer to zero and thus less negative than [tex]\(-1.8\)[/tex].
Therefore, [tex]\(-1.8 > -0.9\)[/tex] is incorrect because [tex]\(-1.8\)[/tex] is more negative. This statement is false.
Given the analysis, we can conclude:
- Statements i and ii are true.
- Statements iii and iv are false.
So, the correct answer is:
i and ii
