Theory of Error & Taping

$****$ Note: Only questions $1$&$2$ are about significant figures. No need to apply significant figures rules in other questions.$**$

$****$ Note: Please note that in taping questions, based on discussion during lectures you must determine a reasonable and rational nominal tape length, then solve those questions$**$

$1-$ How many significant figures are there in the following numbers?

$\backslash$table$[[4324,0\mathrm{.}036,51\mathrm{.}721,0\mathrm{.}0132],[300\mathrm{.}00,,820031,350\mathrm{.}1],[538400,,,3630.]]$

$2-$ Find the followings and apply significant figures rules.

a$.$ Sum of $0\mathrm{.}961,20\mathrm{.}53,82\mathrm{.}3,23\mathrm{.}7245$

b$.$ Product of $324\mathrm{.}98,28\mathrm{.}7$

$3-$ A student counted $133,129,128,132,130,$ and $126$ paces in six trials of walking along a typical course on level ground. Then $342,344,339,$ and $338$ paces were counted in walking four repetitions of an unknown distance $AB.$

What is $($a$)$ the pace length and $($b$)$ the length of $AB?$

$4-$ For the following data, compute the horizontal distance for a recorded slope distance $AB.$

a$)AB=385\mathrm{.}31ft,$ slope angle $=9{11}^{\text{'}}{30}^{\text{'}\text{'}}$

b$)AB=210\mathrm{.}75m,$ difference in elevation $A$ to $B=-5\mathrm{.}454m.$

$5-$ A distance of $543\mathrm{.}33ft.$ was measured with a $100\mathrm{.}00ft.$ tape $($actual and nominal tape lengths are the same$)$ in temperature of $97F.$ What is the correct length?

$6-$ The length of a line is measured as $488\mathrm{.}4ft.$ and the actual tape length is found to be $99\mathrm{.}95ft.$ What is the correct length of the line? Temperature is $68$ degrees of Fahrenheit.

$7-$ A tape with actual length of $100\mathrm{.}06$ is used for measurement of a line $($A to B$)$ in two segments. The full tape length covered segment $1$ which was measured in $92F.$ Segment $2$ was measured in $33F$ and found to be $75\mathrm{.}4ft.$ What is the correct length between $A$ to $B?$

$8-$ A tape with $100\mathrm{.}11ft$ actual length is used to measure a line on a slope in $81F.$ The slope distance measurement was found to be $843\mathrm{.}5ft.$ The elevation difference is $7\mathrm{.}4ft.$ What is the corrected horizontal length between the end points of that line?