9514 1404 393
Answer:
a. 2/3
Step-by-step explanation:
The bar over the 6 means the digit is repeated indefinitely. A bit of algebra can turn a repeating decimal into a fraction. Let x represent the value of the repeating decimal.
[tex]x=0.6\overline{6}\\\\10x=6.6\overline{6}\\\\10x-x=6.6\overline{6}-0.6\overline{6}\\\\9x=6\\\\x=\dfrac{6}{9}=\boxed{\dfrac{2}{3}}[/tex]
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The attachment shows the long division of 2/3 gives a repeating decimal with a repeating digit of 6. You can tell the quotient repeats when the new dividend (after subtraction) is equal to a dividend you have seen before. In this case, the dividend is repeatedly 20, and the quotient digit is repeatedly 6.
The point of the long division is to show you that 2/3 is the correct answer choice for a rational number equivalent to 0.666...(repeating).
