Uncertainty

The following three measurements of length are given: $L_{1}=22.05m, L_{2}=6.1123m$, and $L_{3}=89.6m$. What is the sum of these measurements using rules of proper significant digits?

(A) 120 $m$
(B) 118 $m$
(C) 117.8 $m$
(D) 117.76 $m$
(E) 117.7623 $m$

The following two measurements of length are recorded from an experiment: $L_{1}=4.57\times 10^{3}m$ and $L_{2}=2.130\times 10^{2}m$. Using the rules of significant digits, what is the sum $(L_{1}+L_{2})$ of these measurements?

(A) $5\times 10^{3}m$
(B) $4.8\times 10^{3}m$
(C) $4.78\times 10^{3}m$
(D) $4.783\times 10^{3}m$
(E) $6.70\times 10^{3}m$

A solid rectangular box is measured to have length $L=13.34$ cm, width $W=8.45$ cm, and height $H=3.36$ cm. Which one of the following choices best represents the volume of the box using proper significant digits?

(A) $4\times 10^{2}$ cm $^3$
(B) $3.8\times 10^{2}$ cm $^3$
(C) $3.79\times 10^{2}$ cm $^3$
(D) $3.787\times 10^{2}$ cm $^3$
(E) $3.7875\times 10^{2}$ cm $^3$

Which one of the following choices represents the measurement with the most number of significant digits?

(A) 6.75 $m$
(B) $4.67\times 10^{9}m$
(C) 0.000000012 $m$
(D) 8100 $m$
(E) 2.00005 $m$

In the laboratory, a student makes the following six measurements for the length of an object: 5.05 cm,5.06 cm, 5.07cm, 5.06 cm, 5.07 cm, and 5.09 cm. Using the rules of significant digits, which one of the following choices correctly represents how she should express the average length of the object?

(A) 5 cm
(B) 5.06 cm
(C) $5.06$ cm
(D) 5.07 cm
(E) 5.1 cm

Two length measurements are made and recorded as $L_{1}=84.55$ cm and $L_{2}=33.55$ cm. Two other length measurements are made and recorded as $L_{3}=1.750$ cm and $L_{4}=1.250$ cm. These measurements are used to compute the quantity $(L_{1}+L_{2})-(L_{3}+L_{4})$ using the rules of significant figures. Which one of the following choices best represents the correct result to this calculation?

(A) 115.100 cm
(B) 115.10 cm
(C) 115.1 cm
(D) 115 cm
(E) 120 cm

The following four length measurements are recorded: $5.4\times 10^{-1}m, 5.4\times 10^{0}m, 5.40\times 10^{1}m$, and 5.400 $\times 10^{2}m$. Which one of the following choices best represents the sum of these values using the rules of significant digits?

(A) $6\times 10^{2}m$
(B) 6. $0\times 10^{2}m$
(C) 6. $00\times 10^{2}m$
(D) $5.999\times 10^{2}m$
(E) $5.9994\times 10^{2}m$

The following lengths are added together: $L_{1}=8.36\times 10^{1}m, L_{2}=9.20\times 10^{2}m, L_{3}=1.39\times 10^{-1}m,$ and $L_{4}=2.1\times 10^{0}m$. How many significant digits are in the resulting sum?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 7

What is the percent uncertainty in the measurement $2.54\pm 0.16$ cm?

(A) 2.9%
(B) 6.3%
(C) 8.7%
(D) 12.6%
(E) 14%

A sphere has a radius of1.96 $\pm 0.01m$. What is the approximate uncertainty in its volume?

(A) $31.5\pm 0.2m^{3}$
(B) $31.5\pm 0.3m^{3}$
(C) $31.5\pm 0.4m^{3}$
(D) $31.5\pm 0.5m^{3}$
(E) $31.5\pm 0.6m^{3}$