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).
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