To determine which statements are true, we’ll compare each pair of rational numbers:
### Statement i: [tex]\(-3.4 < -5.2\)[/tex]
To compare [tex]\(-3.4\)[/tex] and [tex]\(-5.2\)[/tex], observe their positions on the number line. A number is smaller if it is further to the left. Since [tex]\(-5.2\)[/tex] is to the left of [tex]\(-3.4\)[/tex], [tex]\(-5.2\)[/tex] is actually less than [tex]\(-3.4\)[/tex].
Hence, [tex]\(-3.4 < -5.2\)[/tex] is False.
### Statement ii: [tex]\(-4.3 > -4.7\)[/tex]
For [tex]\(-4.3\)[/tex] and [tex]\(-4.7\)[/tex], consider their positions again. Since [tex]\(-4.3\)[/tex] is to the right of [tex]\(-4.7\)[/tex], it means that [tex]\(-4.3\)[/tex] is greater than [tex]\(-4.7\)[/tex].
Therefore, [tex]\(-4.3 > -4.7\)[/tex] is True.
### Statement iii: [tex]\(-1.8 < -0.9\)[/tex]
Compare [tex]\(-1.8\)[/tex] and [tex]\(-0.9\)[/tex]. On the number line, a number further to the left is smaller. Since [tex]\(-1.8\)[/tex] is to the left of [tex]\(-0.9\)[/tex], [tex]\(-1.8\)[/tex] is less than [tex]\(-0.9\)[/tex].
Thus, [tex]\(-1.8 < -0.9\)[/tex] is True.
### Statement iv: [tex]\(-4.7 > -1.8\)[/tex]
Compare [tex]\(-4.7\)[/tex] and [tex]\(-1.8\)[/tex]. A number to the right on the number line is larger. Since [tex]\(-1.8\)[/tex] is to the right of [tex]\(-4.7\)[/tex], it means that [tex]\(-1.8\)[/tex] is greater than [tex]\(-4.7\)[/tex].
Thus, [tex]\(-4.7 > -1.8\)[/tex] is False.
### Summary of True Statements
- ii: [tex]\(-4.3 > -4.7\)[/tex] is True
- iii: [tex]\(-1.8 < -0.9\)[/tex] is True
So, the correct option would be:
- ii and iii
Therefore, the valid answer is:
### ii and iii
