Answer :
To determine which set of numbers is arranged in increasing order, we need to consider the approximate numerical values of the four given numbers: π (pi), \(\sqrt{10}\) (the square root of 10), 3.14, and \(\frac{22}{7}\).
1. Approximate values:
- π (pi) ≈ 3.141592653589793
- \(\sqrt{10}\) ≈ 3.1622776601683795
- 3.14 is already given.
- \(\frac{22}{7}\) ≈ 3.142857142857143
2. Sort the numbers in increasing order:
- 3.14 ≈ 3.14 (given directly)
- π ≈ 3.141592653589793
- \(\frac{22}{7}\) ≈ 3.142857142857143
- \(\sqrt{10}\) ≈ 3.1622776601683795
Therefore, the increasing order of these numbers is:
[tex]\[ 3.14, \pi, \frac{22}{7}, \sqrt{10} \][/tex]
Now, check the given options:
- Option A: \(\pi, \sqrt{10}, 3.14, \frac{22}{7}\)
- Ordering here is incorrect because \(3.14\) is smaller and should appear before π.
- Option B: \(3.14, \pi, \frac{22}{7}, \sqrt{10}\)
- This arrangement matches the increasing order we determined.
- Option C: \(\frac{22}{7}, \sqrt{10}, 3.14, \pi\)
- This ordering is incorrect, as \(\sqrt{10}\) should come after \(\frac{22}{7}\).
- Option D: \(\sqrt{10}, \frac{22}{7}, 3.14, \pi\)
- This ordering is incorrect, as \(\sqrt{10}\) should come last.
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
1. Approximate values:
- π (pi) ≈ 3.141592653589793
- \(\sqrt{10}\) ≈ 3.1622776601683795
- 3.14 is already given.
- \(\frac{22}{7}\) ≈ 3.142857142857143
2. Sort the numbers in increasing order:
- 3.14 ≈ 3.14 (given directly)
- π ≈ 3.141592653589793
- \(\frac{22}{7}\) ≈ 3.142857142857143
- \(\sqrt{10}\) ≈ 3.1622776601683795
Therefore, the increasing order of these numbers is:
[tex]\[ 3.14, \pi, \frac{22}{7}, \sqrt{10} \][/tex]
Now, check the given options:
- Option A: \(\pi, \sqrt{10}, 3.14, \frac{22}{7}\)
- Ordering here is incorrect because \(3.14\) is smaller and should appear before π.
- Option B: \(3.14, \pi, \frac{22}{7}, \sqrt{10}\)
- This arrangement matches the increasing order we determined.
- Option C: \(\frac{22}{7}, \sqrt{10}, 3.14, \pi\)
- This ordering is incorrect, as \(\sqrt{10}\) should come after \(\frac{22}{7}\).
- Option D: \(\sqrt{10}, \frac{22}{7}, 3.14, \pi\)
- This ordering is incorrect, as \(\sqrt{10}\) should come last.
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
