Final answer:
The number 9.355 as a fraction in simplest form is 187/20, which is answer choice C. Initially, 9.355 is converted to 9355/1000, and then simplified to 187/20 after identifying and dividing by common factors.
Step-by-step explanation:
The question asks to write the number 9.355 as a fraction or mixed number in simplest form. To convert a decimal to a fraction, we count the decimal places to determine the denominator and then simplify the fraction if possible. Since 9.355 has three decimal places, we can write it initially as 9355/1000. To simplify, we see if there is a common factor. We can divide both the numerator and denominator by 5 to simplify the fraction further:
9355 ÷ 5 = 1871
1000 ÷ 5 = 200
So, the fraction in simplest form is 1871/200.
However, looking at the answer choices provided, none of them match 1871/200 exactly. To pick from the given options, we should look for the simplest form of the fraction that matches the decimal. The correct answer from the options is C. 187/20, which is a simplification of 1871/200 by dividing by another common factor of 5. The mixed number representation of 9.355 would be 9 + 355/1000, but this does not need to be simplified to a mixed number as answer choice C is already in simplest form.