Sure, here's the long method to solve 300.15 ÷ 23:
1. Add one or more zeros after the decimal point to make the divisor (23) a whole number:
```
300.15 × 10 ÷ 23
```
2. Perform the division as you would normally, ignoring the decimal point for now:
```
1305 ÷ 23 = 56
```
Note: You can use long division or another method of your choice to perform the division.
3. Count the number of decimal places in the dividend (300.15) and subtract the number of decimal places in the divisor (0) to get the number of decimal places in the quotient:
```
Number of decimal places in dividend: 2
Number of decimal places in divisor: 0
2 - 0 = 2
```
Therefore, the quotient has two decimal places.
4. Insert the decimal point in the quotient, counting from the right side and using the number of decimal places calculated in step 3:
```
56.52
```
Therefore, 300.15 ÷ 23 = 56.52 (rounded to two decimal places).