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Which number is equivalent to [tex]\frac{7}{11}[/tex]?

A. 0.63
B. [tex]0 . \overline{63}[/tex]
C. [tex]0 . \overline{6}[/tex]
D. 1.57

Answer :

To solve the problem, we start by expressing the fraction in decimal form. Consider the fraction

[tex]$$
\frac{7}{11}.
$$[/tex]

When you divide 7 by 11, you obtain

[tex]$$
\frac{7}{11} \approx 0.6363636363636364.
$$[/tex]

This decimal repeats every two digits (63), so it is correctly written as

[tex]$$
0.\overline{63}.
$$[/tex]

Now, examining the choices given:

1. [tex]\(0.63\)[/tex] is slightly less than the computed value.
2. [tex]\(0.\overline{63}\)[/tex] is exactly the decimal representation of [tex]\(\frac{7}{11}\)[/tex].
3. [tex]\(0.\overline{6}\)[/tex] (which equals [tex]\(0.6666\ldots\)[/tex]) is different.
4. [tex]\(1.57\)[/tex] is clearly not equivalent.

The comparison shows that the number equivalent to [tex]\(\frac{7}{11}\)[/tex] is

[tex]$$
\boxed{0.\overline{63}}.
$$[/tex]

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