Answered

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

Sagot :

GinnyAnswer
Let's compare the rational numbers and determine which comparisons are true step-by-step.

1. Comparison i. [tex]\(-4.3 < -3.7\)[/tex]

- When comparing negative numbers, the number that is farther to the left on the number line is the smaller number.
- Since [tex]\(-4.3\)[/tex] is farther to the left than [tex]\(-3.7\)[/tex] on the number line, it means [tex]\( -4.3 < -3.7 \)[/tex].
- Therefore, this comparison is true.

2. Comparison ii. [tex]\(-3.7 < -2.6\)[/tex]

- Following the same logic as above, since [tex]\(-3.7\)[/tex] is farther to the left than [tex]\(-2.6\)[/tex] on the number line, it means [tex]\(-3.7\)[/tex] is less than [tex]\(-2.6\)[/tex].
- Therefore, this comparison is true.

3. Comparison iii. [tex]\(-4.3 > -2.6\)[/tex]

- Again, using the number line, [tex]\(-4.3\)[/tex] is farther to the left than [tex]\(-2.6\)[/tex] which means [tex]\(-4.3\)[/tex] is less than [tex]\(-2.6\)[/tex], not greater.
- Therefore, this comparison is false.

4. Comparison iv. [tex]\(-1.8 > -0.9\)[/tex]

- When comparing negative numbers, the one closer to zero is the larger number.
- Since [tex]\(-1.8\)[/tex] is farther from zero than [tex]\(-0.9\)[/tex], it is smaller.
- Therefore, this comparison is false.

Based on the analysis, the true comparisons are i. [tex]\(-4.3 < -3.7\)[/tex] and ii. [tex]\(-3.7 < -2.6\)[/tex].

So, the correct answer is:

- i and ii
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