Significant figures would certainly be quantitative. I am not sure what a qualitative figure would be. Significant digits help to denote the accuracy of the measurement. So they are used in practical measures not in math. Here is what I mean.
If you are doing a math problem 100.00 + 100.00001 you are free to add as many zeros to the end of the number as you want, because it is a number and not a measurement. So the answer could be 200.00001 or 200.000010000 or 200.0000100000000000000. They are identical (equivalent).
Now you go out an actually measure three lengths and find them to be 100.01 feet, 107 feet, and 119 feet and add them together. The addition yields 326.01 feet but the correct answer here is 326 feet with the 6 being uncertain. Here 326 in NOT the same as 236.01 and 236.01 is NOT the same as 236.01000000, etc. The reason being the two non-decimal measurements could be anything from 107.00 to 107.99 and 119.00 and 119.99, so putting anything after the decimal place in the answer would just be, at best, a guess.
The number of significant digits is really pretty straight forward with the exception of figures such as: 2300 this could have 2, 3, or 4 significant figures depending on the actual measurement. Therefor by convention you would play it safe and write it 2.2 x 10 EXP 2.
I hope that helps.