Compare these rational numbers. Which of the following are true?
i. $-4.3<-3.7$
ii. $-3.7<-2.6$
iii. $-4.3>-2.6$
iv. $-1.8>-0.9$
A. iii and iv
B. ii, iii
C. i and ii
D. $i, ii, iii, iv$
Answer (1)
Compare the rational numbers in each inequality.
Determine that − 4.3 < − 3.7 and − 3.7 < − 2.6 are true.
Determine that -2.6"> − 4.3 > − 2.6 and -0.9"> − 1.8 > − 0.9 are false.
Conclude that only i and ii are true, so the answer is ian d ii .
Explanation
Problem Analysis We need to compare the given rational numbers and determine which of the inequalities are true. Let's analyze each inequality separately.
Analyzing Inequality i i. − 4.3 < − 3.7 : This statement is true. On the number line, − 4.3 is to the left of − 3.7 .
Analyzing Inequality ii ii. − 3.7 < − 2.6 : This statement is also true. On the number line, − 3.7 is to the left of − 2.6 .
Analyzing Inequality iii iii. -2.6"> − 4.3 > − 2.6 : This statement is false. On the number line, − 4.3 is to the left of − 2.6 , meaning it is smaller than − 2.6 .
Analyzing Inequality iv iv. -0.9"> − 1.8 > − 0.9 : This statement is false. On the number line, − 1.8 is to the left of − 0.9 , meaning it is smaller than − 0.9 .
Conclusion Therefore, only inequalities i and ii are true.
Examples
Understanding how to compare rational numbers is crucial in many real-life situations. For instance, when managing finances, you might need to compare debt balances. If you owe $4.3 to one person and $3.7 to another, owing 4.3 ( -4.3$) is indeed less preferable than owing 3.7 ( -3.7 ) , i ll u s t r a t in g t ha t -4.3 < -3.7 . S imi l a r l y , co m p a r in g t e m p er a t u res b e l o w zero , l ik e -3.7^\circ C an d -2.6^\circ C$, helps you understand which is colder, reinforcing the concept of comparing negative rational numbers.
