To determine which comparisons between the given pairs of rational numbers are true, let us analyze each statement in detail:
1. Statement (i): [tex]$-4.3 < -3.7$[/tex]
When comparing two negative numbers, remember the number with the smaller absolute value is actually greater. For example, -1 is greater than -5 because -1 is closer to zero.
Here, [tex]$-4.3$[/tex] has a greater magnitude (is more negative) than [tex]$-3.7$[/tex]. Therefore, [tex]$-4.3 < -3.7$[/tex] is indeed true.
2. Statement (ii): [tex]$-3.7 < -2.6$[/tex]
Following the same logic as above, [tex]$-3.7$[/tex] has a greater magnitude (is more negative) than [tex]$-2.6$[/tex]. Therefore, [tex]$-3.7 < -2.6$[/tex] is true.
3. Statement (iii): [tex]$-4.3 > -2.6$[/tex]
Again, consider the magnitudes: [tex]$-4.3$[/tex] is more negative than [tex]$-2.6$[/tex]. This makes [tex]$-4.3$[/tex] less than [tex]$-2.6$[/tex], not greater. Hence, [tex]$-4.3 > -2.6$[/tex] is false.
4. Statement (iv): [tex]$-1.8 > -0.9$[/tex]
Evaluating the magnitudes of these negative numbers, [tex]$-1.8$[/tex] is more negative than [tex]$-0.9$[/tex]. This means [tex]$-1.8$[/tex] is less than [tex]$-0.9$[/tex], not greater. Thus, [tex]$-1.8 > -0.9$[/tex] is false.
Based on the above analysis, the statements that are true are:
- i. [tex]$-4.3 < -3.7$[/tex]
- ii. [tex]$-3.7 < -2.6$[/tex]
Thus, the true comparisons are:
i and ii.
