Question

x=(a² b²) ÷ (c³d³)
if error in a=1% b=2% c=3% d=4% then find percentage error in x.​

Answer 1

Given

x=

C

3

1

D

3

A

2

B

2

1

% error ,

x

Δx

×100=2

A

ΔA

×100+

2

1

B

ΔB

×100+

3

1

c

Δc

×100+3

D

ΔD

×100

=2×1%+

2

1

×2%+

3

1

×3%+3×4%

=2%+1%+1%+12%

=16%

Answer 2

Answer:

Given

x=

C

3

1

D

3

A

2

B

2

1

% error ,

x

Δx

×100=2

A

ΔA

×100+

2

1

B

ΔB

×100+

3

1

c

Δc

×100+3

D

ΔD

×100

=2×1%+

2

1

×2%+

3

1

×3%+3×4%

=2%+1%+1%+12%

=16%