Which of the following is the greatest? \[ 0.6, \ 0.666, \ \frac{5}{6}, \ \frac{2}{3} \]
Which of the following is the greatest? \[ 0.6, \ 0.666, \ \frac{5}{6}, \ \frac{2}{3} \]
Show Hint
To compare repeating and terminating decimals, convert them to fractions and compare their values.
0.6
0.666
\( \frac{5}{6} \)
\( \frac{2}{3} \)
The Correct Option is B
Solution and Explanation
Step 1: Convert the decimals to fractions
- 0.6 is equivalent to \( \frac{2}{3} \).
- 0.666 is already a terminating decimal and equals \( \frac{2}{3} \).
- \( \frac{5}{6} \) is in its simplest fractional form.
- \( \frac{2}{3} \) is also in its simplest form.
Step 2: Comparison
- \( 0.6 = \frac{2}{3} \), which is less than 0.666.
- 0.666 is slightly greater than \( \frac{2}{3} \), and is the greatest among the values listed.
Thus, the correct answer is (B).
Top Questions on Trees
A meld operation on two instances of a data structure combines them into one single instance of the same data structure. Consider the following data structures:
P: Unsorted doubly linked list with pointers to the head node and tail node of the list.
Q: Min-heap implemented using an array.
R: Binary Search Tree.
Which ONE of the following options gives the worst-case time complexities for meld operation on instances of size \( n \) of these data structures?- In a B+- tree where each node can hold at most four key values, a root to leaf path consists of the following nodes: \( A = (49, 77, 83, -) \)
\( B = (7, 19, 33, 44) \)
\( C = (20^*, 22^*, 25^*, 26^*) \)
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- Suppose the values 10, −4, 15, 30, 20, 5, 60, 19 are inserted in that order into an initially empty binary search tree. Let \( T \) be the resulting binary search tree. The number of edges in the path from the node containing 19 to the root node of \( T \) is \underline{{1cm}}. {(Answer in integer)}
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