#JavaScript (ES6), 94 bytes

Not particularly short, but fun. Adding parentheses all over the place...

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    s=>([e,o]=s.split` `,[...o].map(x=>e=e.split(x).join((a+=')')+x+(b+='(')),a=b=''),eval(b+e+a))

###Test cases

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    let f =

    s=>([e,o]=s.split` `,[...o].map(x=>e=e.split(x).join((a+=')')+x+(b+='(')),a=b=''),eval(b+e+a))

    console.log(f("6.3*7.8 +-*/"))              // 49.14
    console.log(f("2.2*3.3+9.9/8.8-1.1 */+-"))  // 7.285
    console.log(f("2.2*3.3+9.9/8.8-1.1 +*/-"))  // 2.2
    console.log(f("10/2+5-1 +-/*"))             // 1.6666
    console.log(f("2147480/90+10*5 +/-*"))      // 107374
    console.log(f("3*55-5/8/4+1 -/+*"))         // 7.6875


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