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Which choice is equal to the fraction below?
[tex]\[ \frac{8}{9} \][/tex]

A. [tex]\[ 0.88888888 \ldots \][/tex]

B. [tex]\[ 0.8 \][/tex]

C. [tex]\[ 0.888 \][/tex]


Sagot :

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.
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