Write $13.395$ and $22.8642$ in Stevin's notation. Use his rules to multiply the two numbers together and to divide the second by the first.

Step 1: Convert the numbers into Stevin's notation To convert the given numbers, $13.395$ and $22.8642$, into Stevin's notation, we need to write them as whole numbers followed by a separator (like a comma), and then write out the decimals with the fractional part as a numerator, and the power of 10 they represent as the denominator. As follows: 13.395$inStevi{n}^{\prime }snotation:$13, \frac{395}{1000}22.8642$inStevi{n}^{\prime }snotation:$22, \frac{8642}{10000} Step 2: Multiply the numbers using Stevin's rules To multiply the numbers in Stevin's notation, we will follow these steps: 1. Multiply the whole parts of the numbers: $13\times 22=286$ 2. Multiply the fractional parts of the numbers: $\frac{395}{1000}\times \frac{8642}{10000}=\frac{3410890}{10000000}$ 3. Multiply the whole part of the first number by the fractional part of the second number, and vice versa, and add the products: $13\times \frac{8642}{10000}+22\times \frac{395}{1000}=\frac{112346}{1000}+\frac{8690}{1000}=\frac{121036}{1000}$ 4. Add all the results: $286,\frac{3410890}{10000000}+\frac{121036}{1000}=286,\frac{3410890+121036000}{10000000}=286,\frac{124346890}{10000000}$ So, the product of $13.395$ and $22.8642$ in Stevin's notation is 286, \frac{12434689}{1000000}$.Step3:DividethesecondnumberbythefirstusingStevi{n}^{\prime }srulesTodividethesecondnumberbythefirstinStevi{n}^{\prime }snotation,wewillfollowthesesteps:1.Dividethewholepartsofthenumbers:22÷13=1$ 2. Find the remainder of the whole parts: $22-(13\times 1)=9$ (This remainder will be used with the first fractional part in the next step) 3. Divide the fractional parts: $\frac{8642-(395\times 1)}{10000}=\frac{8247}{10000}$ 4. Divide the remainder of the whole parts by the whole part of the divisor and combine it with step 3 result: $\frac{9}{13}+\frac{8247}{10000}=\frac{9}{13}+\frac{8247}{10000}\cdot \frac{13}{13}=\frac{9}{13}+\frac{107211}{130000}=\frac{219402}{130000}$ The quotient in Stevin's notation when dividing $22.8642$ by $13.395$ is 1, \frac{219402}{130000}.