For your ML system, you are thinking about how to represent matrices and are concerned with the storage cost.
You are unsure whether to use a dense or sparse representation. The two options are a row-major dense matrix or a modified compressed sparse row matrix (MCSR).
Your matrix cells store float values of 32 bit size. The sparse representation consists of an array of pointers (64 bit) to 2-array-data-structures for the index and value. The indices are stored as 32 bit integers and the values as 32 bit floats. Assume the data structure itself has no additional memory requirements, i.e. it is simply two arrays.
Your matrix size is always 1200 x 900 (rows x columns).
What is fraction of cells that need to be filled for the dense representation to have the same memory consumption as the sparse representation? Use four decimal point precision for the degree, e.g. 0.1234 (number between 0 and 1)