Step one: 63 marks out of 70 on the final exam
A final exam scored 63 out of 70 raw marks converts to a percentage of (63 ÷ 70) × 100 = 90% — a letter grade of A on its own, before it's combined with anything else from the course.
Step two: feeding that 90% into the weighted course grade
With an assignment score of 82% weighted at 20% and a midterm score of 76% weighted at 30%, adding that 90% final exam result at a 50% weight gives (82×20 + 76×30 + 90×50) ÷ 100 = 84.2% overall — a letter grade of B, even though the final exam itself scored an A.
How sensitive the overall grade is to the final exam: 62 out of 70 instead
Just one mark lower on the final — 62 out of 70 rather than 63 — converts to (62 ÷ 70) × 100 = 88.57%, still a B on its own. Feeding that into the same weighted calculation, (82×20 + 76×30 + 88.57×50) ÷ 100 = 83.49% overall, a difference of 0.71 percentage points in the final course grade from a single raw mark on the exam — a direct result of the final exam carrying half the total weight.
Why converting to a percentage first is the right order of operations
A weighted grade calculation expects every component on the same percentage scale, but a final exam's raw mark sheet rarely is — it might be out of 70, 100, or 150 depending on the course. Converting the raw marks to a percentage before entering it as the "final exam score" component is what keeps the weighting meaningful: a 50% weight is only accurate if the number being weighted is actually a percentage, not a raw mark count out of some other total.