Let's determine which of the given choices is equal to the fraction [tex]\(\frac{8}{9}\)[/tex].
First, let's understand the value of [tex]\(\frac{8}{9}\)[/tex]:
[tex]\[\frac{8}{9}\][/tex]
We need to compare this with the given choices:
- A. [tex]\(0.88888888 \ldots\)[/tex]
- B. [tex]\(0.8\)[/tex]
- C. [tex]\(0.888\)[/tex]
Step-by-step comparison:
1. Choice A: [tex]\(0.88888888 \ldots\)[/tex]
This is a repeating decimal that continues indefinitely. To check if it is equal to [tex]\(\frac{8}{9}\)[/tex], let’s compare the decimal representation:
[tex]\[\frac{8}{9} = 0.88888888 \ldots\][/tex]
This shows that [tex]\(\frac{8}{9}\)[/tex] has the same repeating decimal form as choice A.
2. Choice B: [tex]\(0.8\)[/tex]
This is a finite decimal and does not repeat. Clearly, [tex]\(\frac{8}{9}\)[/tex] which is equal to [tex]\(0.88888888 \ldots\)[/tex] is not equal to [tex]\(0.8\)[/tex].
3. Choice C: [tex]\(0.888\)[/tex]
This is also a finite decimal. Although it might seem similar, [tex]\(0.888\)[/tex] does not repeat and thus does not match the value of [tex]\(\frac{8}{9}\)[/tex]. The correct representation of [tex]\(\frac{8}{9}\)[/tex] is a repeating decimal that continues indefinitely, not a finite decimal.
From the above comparisons, we find that:
[tex]\[\frac{8}{9} = 0.88888888 \ldots\][/tex]
Therefore, the correct choice is:
[tex]\[A. \, 0.88888888 \ldots\][/tex]
So, the answer is Choice A.
