Alright, let's compare these rational numbers step by step.
### i. [tex]$-2.3 > -1.3$[/tex]
To determine if [tex]$-2.3$[/tex] is greater than [tex]$-1.3$[/tex], consider their positions on the number line. Both numbers are negative, and in the context of negative numbers, a number with a smaller absolute value is greater. Clearly, [tex]$-2.3$[/tex] has a larger absolute value than [tex]$-1.3$[/tex], meaning it is further to the left on the number line. Thus:
[tex]\[ -2.3 < -1.3 \][/tex]
Therefore, the statement [tex]\( -2.3 > -1.3 \)[/tex] is false.
### ii. [tex]$-2.3 < -1.3$[/tex]
As discussed in the previous comparison, since [tex]$-2.3$[/tex] is further to the left on the number line compared to [tex]$-1.3$[/tex], we can confirm:
[tex]\[ -2.3 < -1.3 \][/tex]
Therefore, the statement [tex]\( -2.3 < -1.3 \)[/tex] is true.
### iii. [tex]$-2.3 > -3.3$[/tex]
Next, let's compare [tex]$-2.3$[/tex] and [tex]$-3.3$[/tex]. Comparing their absolute values, [tex]$-3.3$[/tex] has a larger absolute value than [tex]$-2.3$[/tex], meaning [tex]$-3.3$[/tex] is further to the left on the number line. Therefore:
[tex]\[ -2.3 > -3.3 \][/tex]
Thus, the statement [tex]\( -2.3 > -3.3 \)[/tex] is true.
### iv. [tex]$-2.3 < -3.3$[/tex]
Based on the previous comparison, we established that [tex]$-2.3$[/tex] is to the right of [tex]$-3.3$[/tex] on the number line, meaning:
[tex]\[ -2.3 > -3.3 \][/tex]
Thus, the statement [tex]\( -2.3 < -3.3 \)[/tex] is false.
### Summary
- [tex]\( -2.3 > -1.3 \)[/tex]: false
- [tex]\( -2.3 < -1.3 \)[/tex]: true
- [tex]\( -2.3 > -3.3 \)[/tex]: true
- [tex]\( -2.3 < -3.3 \)[/tex]: false
Hence, the results are:
[tex]\[ (False, True, True, False) \][/tex]
