Decimal Multiplication of Strings

Java 7, 89

void g(char[]a,float b){for(int i=0,l=a.length;i<(int)(l*b);)System.out.print(a[i++%l]);}

takes char[] and float and outputs to STDOUT. basic looping.

JavaScript (ES6), 50 bytes

Edit 2 bytes more to include definition of function f. 1 byte less using the tip of @manatwork. Note: using ~ we have more iterations than necessary, but this is code golf and even 1 byte counts

f=(s,n,l=s.length*n)=>~n?f(s+s,n-1,l):s.slice(0,l)

TEST

f=(s,n,l=s.length*n)=>~n?f(s+s,n-1,l):s.slice(0,l)

//TEST
console.log=x=>O.textContent+=x+'\n'
;[
 ['test case', 1, 'test case'],
 ['case', 3.5, 'casecasecaseca'],
 ['(will add more later)', 0.3333, '(will '],
 ['cats >= dogs', 0.5, 'cats >']]
.forEach(t=>{
  var s=t[0],n=t[1],x=t[2],r=f(s,n);
  console.log("«"+s+"» "+n+' => «'+r+'» '+(x==r?'OK':'FAIL expected '+x));
 })

<pre id=O></pre>

Pyth, 9 8

s@Lz*lzQ

Saved 1 byte thanks to Pietu1998

This takes floor(n * len(string)) letters from the string, using cyclical indexing. I believe this is always equivalent to the given formula.

Test Suite