Let's determine which of the given decimal values is closest to the fraction [tex]\(\frac{2}{9}\)[/tex].
First, we need to express the fraction [tex]\(\frac{2}{9}\)[/tex] in decimal form. The decimal representation of [tex]\(\frac{2}{9}\)[/tex] is approximately 0.2222.
Next, we will compare this decimal value with the given choices:
- A. 0.4
- B. 0.222
- C. 0.1111
We will calculate the absolute difference between [tex]\(\frac{2}{9}\)[/tex] and each choice to determine which is the closest.
1. Calculate the difference between [tex]\(\frac{2}{9}\)[/tex] and 0.4:
[tex]\[
\left| 0.2222 - 0.4 \right| = 0.1778
\][/tex]
2. Calculate the difference between [tex]\(\frac{2}{9}\)[/tex] and 0.222:
[tex]\[
\left| 0.2222 - 0.222 \right| = 0.0002
\][/tex]
3. Calculate the difference between [tex]\(\frac{2}{9}\)[/tex] and 0.1111:
[tex]\[
\left| 0.2222 - 0.1111 \right| = 0.1111
\][/tex]
Now, we compare the differences:
- The difference with 0.4 is 0.1778
- The difference with 0.222 is 0.0002
- The difference with 0.1111 is 0.1111
The smallest difference indicates the closest value. In this case, the difference with 0.222 (0.0002) is the smallest.
Therefore, the decimal closest in value to [tex]\(\frac{2}{9}\)[/tex] is:
\[
\boxed{0.222}
