Well if you wanna do it by hand, just do the stacking thing. Maybe try again, see if you did something wrong?
$${\mathtt{17.34}}{\mathtt{\,\times\,}}{\mathtt{13}} = {\mathtt{225.42}}$$
17.34
x 13
------------
3*4= 12 3*3+1=10 7*3+1= 22 3*1+2= 5
Your first line of Multiplying is 5202 (ignoring the decimal place for now)
Second line (dont forget the smiley face 0)
1*4=4 1*3=3 1*7=7 1*1=1
Your second line looks like 17340
Now whats 17340+5202=22542
Now add the decimal places in, two from the right
225.42 and i checked the calculator and thats right