what is the correct way to write a decimal in a fraction? For example 1.5/24.
What you should try to do first is convert the decimal to a fraction.
We know that $\displaystyle .5=\tfrac{1}{2}$
Thus $\displaystyle 1.5=1+.5=1+\tfrac{1}{2}=\tfrac{3}{2}$
So, we see that $\displaystyle \frac{1.5}{24}=\frac{\tfrac{3}{2}}{24}$
I hope you can take it from here.
--Chris
A general procedure to get rid of the decimal point is to multiply the number by a power of 10 with as many zero digits as the number has digits after the decimal point - and then divide the product by the power of 10 you used. An example:
$\displaystyle 1.234 = \frac{1.234 \cdot 1000}{1000} = \frac{1234}{1000}$
With your example:
$\displaystyle \frac{1.5}{24} = \frac{1.5}{24} \cdot \frac{10}{10} = \frac{15}{240}$
BTW there is no "correct way", just the way the nagging old fusspot of a teacher wants it.
1.5 / 24 is perfectly "correct", just that it may not be in those hallowed "lowest terms" that daft old loonies get all het up about and start throwing chalk dusters around the room if you get it "wrong".