Compare these rational numbers. Which of the following are true?

i. [tex]\(-4.3 \ \textless \ -3.7\)[/tex]
ii. [tex]\(-3.7 \ \textless \ -2.6\)[/tex]
iii. [tex]\(-4.3 \ \textgreater \ -2.6\)[/tex]
iv. [tex]\(-1.8 \ \textgreater \ -0.9\)[/tex]

A. i and ii
B. iii and iv
C. ii, iii
D. i, ii, iii, iv



Answer :

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.