To express the fraction [tex]\(\frac{9}{41}\)[/tex] as a decimal, you divide the numerator (9) by the denominator (41). This division will give you a repeating or terminating decimal.
After performing the division, the result is approximately [tex]\(0.21951219512195122\)[/tex].
From this result, we can see that the decimal value is neither exactly [tex]\(0.21951\)[/tex] nor fits perfectly into any of the given repeating patterns.
None of the provided repeating decimal forms - [tex]\(0.219 \overline{51}\)[/tex], [tex]\(0 . \overline{21951}\)[/tex], and [tex]\(0.21 \overline{951}\)[/tex] – match exactly.
So, while the result matches approximately [tex]\(0.21951\)[/tex] up to five decimal places, it continues beyond that and does not fit into a simple repeating pattern.
Thus, the closer possible answer to [tex]\(\frac{9}{41}\)[/tex] expressed as a decimal from the given choices is:
[tex]\[ 0.21951 \][/tex]
However, it's important to remember that this is an approximation and the actual decimal value is more precise.
