If a table is round and its diameter is determined to 1%, how well is the area known?

The length of the measurement, or whether it is radius or diameter or circumference does not matter, 1% is still 1%!!

With a 1% diameter (or radius or circumference), the area is known to 2% and this can be proven as follows:

for radius:

A = πr²

A' = π(1.01r)²

A'/A = (1.01r)² / r² = (1.01)² = 1.02

for diameter:

A = π(d/2)²

A' = π(1.01d/2)²

A'/A = (1.01d)² / d² = (1.01)² = 1.02

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99% ONE PERCENT is a constant......doesnt matter how long it is. For example: 1% of 100 = 1 and 1 % of 200 = 2 .......so If you took 99% of 200 which is 198 and multiplied it by 2 you would get 396 which is 1% OFF the RIGHT answer of 400.. (for 200 x 2).....likewise if you took 99% of 100 which is 99 and multiplied it by 2 it would = 198 which is also 1% off the RIGHT answer of 200..(for 100 x 2) You See it is CONSTANT........