Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.