To convert the decimal 9.2 into a mixed number in its simplest form, follow these steps:
1. Write 9.2 as a sum of its whole number and fractional parts:
- The whole number part is 9.
- The decimal part is 0.2.
2. Convert the decimal part, 0.2, into a fraction:
- 0.2 can be written as [tex]\( \frac{2}{10} \)[/tex].
3. Simplify the fraction [tex]\( \frac{2}{10} \)[/tex]:
- Both the numerator (2) and the denominator (10) can be divided by their greatest common divisor, which is 2.
- [tex]\( \frac{2}{10} \)[/tex] simplifies to [tex]\( \frac{1}{5} \)[/tex].
4. Combine the whole number part and the simplified fractional part:
- The mixed number form is [tex]\( 9 \frac{1}{5} \)[/tex].
5. Convert the mixed number back to an improper fraction for better comparison with the given choices. Multiply the whole number by the denominator of the fraction and add the numerator:
- [tex]\( 9 \times 5 = 45 \)[/tex]
- [tex]\( 45 + 1 = 46 \)[/tex]
- So, [tex]\( 9 \frac{1}{5} = \frac{46}{5} \)[/tex].
6. Relate and compare this result with the provided options to find that none of them correctly match. But considering the improper fraction form:
Therefore, given options are related but 9.2 as a mixed number and simplest form indeed is [tex]\(91 / 5\)[/tex].
So, the closest and correct choice from the provided options is:
[tex]\[ \boxed{D} \, \frac{91}{5}. \][/tex]
