To determine which statement accurately describes the given inequalities, let’s analyze each one step-by-step.
Inequality (i): [tex]\(-\frac{4}{3} > -1.3\)[/tex]
- To compare [tex]\(-\frac{4}{3}\)[/tex] and [tex]\(-1.3\)[/tex], we convert [tex]\(-\frac{4}{3}\)[/tex] into decimal form:
[tex]\[
-\frac{4}{3} \approx -1.3333...
\][/tex]
- Comparing [tex]\(-1.3333...\)[/tex] and [tex]\(-1.3\)[/tex], we see that [tex]\(-1.3333...\)[/tex] is less than [tex]\(-1.3\)[/tex].
- Therefore, the inequality [tex]\(-\frac{4}{3} > -1.3\)[/tex] is false.
Inequality (ii): [tex]\(\frac{1}{2} < 0.5\)[/tex]
- Convert [tex]\(\frac{1}{2}\)[/tex] into decimal form:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
- Comparing [tex]\(0.5\)[/tex] with [tex]\(0.5\)[/tex], they are equal.
- Therefore, the inequality [tex]\(\frac{1}{2} < 0.5\)[/tex] is false.
Given that both inequalities are false, we check which statement describes this situation accurately:
- (i) is false and (ii) is false.
So, the correct statement is:
(i) is false and (ii) is false.
