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Expectation of life is the average number of further years lived. Under a constant annual mortality rate the curtate expectation collapses to pₓ/qₓ, and adding half a year gives the complete expectation that allows for deaths part-way through a year.
Constant-force expectation
eₓ = p/q; e°ₓ = eₓ + 0.5; ₁₀pₓ = p^10
Curtate expectation counts only whole years survived. Deaths occur on average mid-year, so the complete figure adds about 0.5.
Only over short spans. Real mortality rises steeply with age, so a full life table gives a better answer at older ages.