Question

Which choice best describes the degree of uncertainty in the measurement of 16.30 g?
(a) The uncertainty cannot be determined without additional information
(b) The quantity is exact
(c) + 0.10 g
(d) + 0.01 g
​

Answer 1

Answer:

Correct option is

A

164±3cm

2

Error in product of quantities: Suppose x=a×b

Let Δa=absolute error in measurement of a,

Δb=absolute error in measurement of b,

Δx=absolute error in calculation of x, i.e. product of a and b.

The maximum fractional error in x is

x

Δx

=±(

a

Δa

+

b

Δb

)

Percentage error in the value of x=(Percentage error in value of a)+(Percentage error in value of b)

According to the problem, length l=(16.2±0.1)cm

Breadth b=(10.1±0.1)cm

Area A=l×b=(16.2cm)×(10.1cm)=163.62cm

2

As per the rule area will have only three significant figures and error will have only one significant figure.Rounding off we get,area A=164cm

2

If ΔA is error in the area, then relative error is calculated as

A

δ4

.

A

Δ4

=

l

Δl

+

b

Δb

=

16.2cm

0.1cm

+

10.1cm

0.1cm

=

16.2×10.1

1.01+1.62

=

163.62

2.63

⇒ΔA=A×

163.62

2.63

cm

2

=162.62×

163.62

2.63

=2.63cm

2

ΔA=3cm

2

(By rounding off to one significant figure)

Area, A=A±ΔA(164±3)cm

2