Find the number in the Champernowne constant
LabVIEW, 29 LabVIEW Primitives
This uses strings for now. It matches the input as a pattern and outputs the offset - (input lenght -1).
Pyth, 10
hxjkS+QT`Q
Concatenates first input + 10
numbers then finds the 0 based index plus one.. The extra ten are only needed for 0.
Test Suite
Javascript, 57 bytes
a=prompt();for(y=b=" ";y<a+11;)b+=++y;alert(b.indexOf(a))
Saved 1 byte thanks to Conor O'Brien.