Question

Th random errors associated with the measurement of p and q are 10% and 2% what is the percentage random error in p/q

Answer 1

We have to find out error In P/q
Let y = P/q
now, differentiate both sides,
dy = (qdp - pdq)/q²
dy = dp/q - pdq/q²
dy/y = dp/q×p/q - pdq/q × p/q
dy/y = dp/p - dq/q
Hence, ∆y/y = ∆P/P - ∆q/q
But in case of finding error we have to use always positive terms [ because we want to find maximum error ]
so, ∆y/y = ∆P/P + ∆q/q
∴ % error in y = % error in p + % error in q
= 10 % + 2%
= 12%

Hence, answer is 12%

Answer 2

Percentage error is additive in nature in case of Multiplying and Division
Let z = p/q
=>Δz/z = Δp/p + Δq/q
=> Δz/z × 100 = Δp/p × 100 + Δq/q × 100
=> Percentage Error = 10 % + 2%
=> Percentage Error = 12%
This is the required Percentage Error