Calculations with binomial and decimal conversions

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1KB=$2^{10}$ Bytes and somehow 1KB/sec=$10^3$ Bytes/sec. If you cancel out the sec$^{-1}$ on the second equation you get 1KB=$10^3$ Bytes. Can you please explain this to me? This is messing up all my homework conversions. How does dividing a unit by seconds change it from binomial to decimal conversions?

The conflict that doesn't make sense to me is how: 1KB = $2^{10}$B, but 1Mbps = $10^6$.