What is the correct increasing order of \(\frac{7}{4}\), \(\sqrt{3}\), and \(1.76\) on the number line?
Answer and explanation
Correct answer: \(\sqrt{3},\frac{7}{4},1.76\)
The governing concept is comparison of different forms of real numbers by converting them to comparable approximations. We have \(\frac{7}{4}=1.75\), \(\sqrt{3}\approx1.732\), and the given decimal is 1.76. Comparing these values gives \(1.732<1.75<1.76\). Therefore the increasing order is \(\sqrt{3},\frac{7}{4},1.76\), which is option A. Option B reverses the first two values, while options C and D place the largest or middle number incorrectly. The approximation is sufficient because the values are separated clearly.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{3},\frac{7}{4},1.76\)
Why is this the correct answer?
The governing concept is comparison of different forms of real numbers by converting them to comparable approximations. We have \(\frac{7}{4}=1.75\), \(\sqrt{3}\approx1.732\), and the given decimal is 1.76. Comparing these values gives \(1.732<1.75<1.76\). Therefore the increasing order is \(\sqrt{3},\frac{7}{4},1.76\), which is option A. Option B reverses the first two values, while options C and D place the largest or middle number incorrectly. The approximation is sufficient because the values are separated clearly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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