To determine the numerator of the fraction that corresponds to the decimal 1.63 in its simplest form, let's follow these steps:
1. Understand the Decimal Representation:
- The decimal number 1.63 can be expressed as a fraction by placing it over 100: [tex]\( \frac{163}{100} \)[/tex].
2. Simplify the Fraction (if necessary):
- To simplify [tex]\( \frac{163}{100} \)[/tex], we need to check if the numerator and the denominator have any common factors other than 1.
- Since 163 is a prime number and doesn't have any common factors with 100 other than 1, the fraction [tex]\( \frac{163}{100} \)[/tex] is already in its simplest form.
3. Identify the Numerator:
- From the fraction [tex]\( \frac{163}{100} \)[/tex], the numerator is 163.
Thus, Nolan wrote 163 in the numerator of the fraction.
So, the correct answer is:
[tex]\( \boxed{163} \)[/tex]
