To determine which repeating decimal is equal in value to the fraction [tex]\(\frac{7}{9}\)[/tex], let's start by understanding what [tex]\(\frac{7}{9}\)[/tex] is in decimal form.
First, we divide 7 by 9. Performing long division, we get:
1. [tex]\( 7 \div 9 = 0.7777777 \ldots \)[/tex]
This means the decimal form of the fraction [tex]\(\frac{7}{9}\)[/tex] is [tex]\(0.\overline{7}\)[/tex], which repeats indefinitely.
Next, let's compare this repeating decimal with the choices provided:
- A. [tex]\(0.5555555 \ldots\)[/tex] (Repeats with 5)
- B. [tex]\(0.7777777 \ldots\)[/tex] (Repeats with 7)
- C. [tex]\(0.8888888 \ldots\)[/tex] (Repeats with 8)
From our division, we found that [tex]\(\frac{7}{9} = 0.7777777 \ldots\)[/tex].
Therefore, the repeating decimal equal to [tex]\(\frac{7}{9}\)[/tex] is:
B. [tex]\(0.7777777 \ldots\)[/tex]
