An experiment measures quantities x, y, z and then t is calculated from the data as t = xy2z3. If percentage erorrs in x, y and z are respectively 1%, 3%, 2% , then percentage error in t is

∆xx = 1% = 10-2∆yy = 3% = 3×10-2∆zz = 2% = 2×10-2 ⇒t = xy2z3∆tt = ∆xx+2∆yy+3∆zz= 10-2+2×3×10-2+3×2×10-2= 13 × 10-2 = 13%

An experiment measures quantities x, y, z and then t is calculated from the data as t = xy2z3. If percentage erorrs in x, y and z are respectively 1%, 3%, 2% , then percentage error in t is

∆xx = 1% = 10-2∆yy = 3% = 3×10-2∆zz = 2% = 2×10-2 ⇒t = xy2z3∆tt = ∆xx+2∆yy+3∆zz= 10-2+2×3×10-2+3×2×10-2= 13 × 10-2 = 13%

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An experiment measures quantities x, y, z and then t is calculated from the data as $t = \frac{{xy}^{2}}{z^{3}}$ . If percentage erorrs in x, y and z are respectively 1%, 3%, 2% , then percentage error in t is

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$\frac{∆ x}{x} = 1 % = 10^{- 2}$

$\frac{∆ y}{y} = 3 % = 3 \times 10^{- 2}$

$\frac{∆ z}{z} = 2 % = 2 \times 10^{- 2} \Rightarrow t = \frac{{xy}^{2}}{z^{3}}$

$\frac{∆ t}{t} = \frac{∆ x}{x} + 2 \frac{∆ y}{y} + \frac{3 ∆ z}{z}$

$= 10^{- 2} + 2 \times 3 \times 10^{- 2} + 3 \times 2 \times 10^{- 2}$

$= 13 \times 10^{- 2} = 13 %$

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An experiment measures quantities x, y, z and then t is calculated from the data as t = xy2z3. If percentage erorrs in x, y and z are respectively 1%, 3%, 2% , then percentage error in t is

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An experiment measures quantities x, y, z and then t is calculated from the data as $t = \frac{{xy}^{2}}{z^{3}}$ . If percentage erorrs in x, y and z are respectively 1%, 3%, 2% , then percentage error in t is