Measurements and Units

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These are the solutions to the NSSCO past questions on Measurements and Units.
The TI-84 Plus CE shall be used for applicable questions.
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Please use the conversion equation specified in the questions as applicable.
However, if the conversion equation was not given to you, then it is necessary to use these tables.
It is also important to memorize the prefixes and the multiplication factors for the International System of Units.
The three tables are:

Table 1

Metric to Metric Conversions
Prefix	Symbol	Multiplication Factor
yocto	y	$10^{-24}$
zepto	z	$10^{-21}$
atto	a	$10^{-18}$
femto	f	$10^{-15}$
pico	p	$10^{-12}$
nano	n	$10^{-9}$
micro	$\mu$	$10^{-6}$
milli	m	$10^{-3}$
centi	c	$10^{-2}$
deci	d	$10^{-1}$
deka	da	$10^1$
hecto	h	$10^2$
kilo	K	$10^3$
mega	M	$10^6$
giga	G	$10^9$
tera	T	$10^{12}$
peta	P	$10^{15}$
exa	E	$10^{18}$
zetta	Z	$10^{21}$
yotta	Y	$10^{24}$

Table 2

Customary to Customary Conversions
Measurement	Customary	Customary	Unit Conversion Factor
Length	inch (in)	foot (ft)	$12\:inches = 1\:ft$
Length	foot (ft)	yard (yd)	$3\:ft = 1\:yd$
Length	yard (yd)	mile (mi)	$1760\:yd = 1\:mi$
Length	foot (ft)	mile (mi)	$5280\:ft = 1\:mi$
Length	rod/pole	yards (yd)	$1\:rod = 5.5\:yd$
Length	furlong	rod	$1\:furlong = 40\;rod$
Length	fathom	feet (ft)	$1\:fathom = 6\;ft$
Length	league/marine	nautical miles	$1\:league = 3\;nautical\;\;miles$
Mass	pound (lb)	ounce (oz)	$1\:lb = 16\:oz$
Mass	short ton (ton)	pound (lb)	$1\:short\:ton = 2000\:lb$
Mass	long ton	pound (lb)	$1\:long\:ton = 2240\:lb$
Mass	stone	pound (lb)	$1\:\:stone = 14\:lb$
Mass	long ton	stone	$1\:long\:ton = 160\:stones$
Area	acre (acre)	square feet ($ft^2$)	$1\:acre = 43560\:ft^2$
Volume	quart (qt)	pint (pt)	$1\:qt = 2\:pt$
Volume	pint (pt)	cup (cup)	$1\:pt = 2\:cups$
Volume	quart (qt)	cup (cup)	$1\:qt = 4\:cups$
Volume	quart (qt)	fluid ounce (fl. oz)	$1\:qt = 32\:fl.\:oz$
Volume	pint (pt)	fluid ounce (fl. oz)	$1\:pt = 16\:fl.\:oz$
Volume	cup (cup)	fluid ounce (fl. oz)	$1\:cup = 8\:fl.\:oz$
Volume	gallon (gal)	quart (qt)	$1\:gal = 4\:qt$
Volume	gallon (gal)	quart (pt)	$1\:gal = 8\:pt$
Volume	gallon (gal)	cup (cup)	$1\:gal = 16\:cups$
Volume	gallon (gal)	fluid ounce (fl. oz)	$1\:gal = 128\:fl.\:oz$
Volume	gallon (gal)	cubic inches ($in^3$)	$1\:gal = 231\:in^3$

Table 3

Metric to Customary Conversions
Measurement	Metric	Customary	Unit Conversion Factor
Length	meter (m)	foot (ft)	$1\:ft = 0.3048\:m$
Length	kilometer (km)	nautical miles	$1\:nautical\;\;miles = 1.852\;km$
Mass	gram (g)	pound (lb)	$1\:lb = 453.59237\:g$
Mass	metric ton (tonne)	kilogram (kg)	$1\:tonne = 1000\:kg$
Volume	liter or cubic decimeters (L or $dm^3$)	gallons (gal)	$1\:L = 0.26417205\:gal$

(1.) Complete the following.
(a.) 2 km = ....... m
(b.) ....... mg = 12 g
(c.) 25 cm³ = ....... mL
(d.) 0.25 ton = ....... kg

$ \underline{\text{Unity Fraction Method}} \\[3ex] kilo = 10^3 \\[3ex] (a.) \\[3ex] 2\;km * \dfrac{.......m}{.......km} \\[5ex] = 2\;km * \dfrac{10^3\;m}{1\;km} \\[5ex] = 2 * 1000\;m \\[3ex] = 2000\;m \\[5ex] (b.) \\[3ex] milli = 10^{-3} \\[3ex] 12\;g = ?\;mg \\[3ex] 12\;g * \dfrac{.......mg}{.......g} \\[5ex] = 12\;g * \dfrac{1\;mg}{10^{-3}\;g} \\[5ex] = \dfrac{12}{0.001}\;mg \\[5ex] = 12000\;mg \\[5ex] (c.) \\[3ex] L = dm^3 \\[3ex] centi = 10^{-2} \\[3ex] deci = 10^{-1} \\[3ex] \text{First, we shall convert from cm³ to dm³ (L)} \\[3ex] \text{Then, we convert from L to mL} \\[3ex] 25 * cm * cm * cm * \dfrac{...m}{...cm} * \dfrac{...m}{...cm} * \dfrac{...m}{...cm} * \dfrac{...dm}{...m} * \dfrac{...dm}{...m} * \dfrac{...dm}{...m} \\[5ex] = 25 * cm * cm * cm * \dfrac{10^{-2}\;m}{1\;cm} * \dfrac{10^{-2}\;m}{1\;cm} * \dfrac{10^{-2}\;m}{1\;cm} * \dfrac{1\;dm}{10^{-1}\;m} * \dfrac{1\;dm}{10^{-1}\;m} * \dfrac{1\;dm}{10^{-1}\;m} \\[5ex] = \dfrac{25 * 10^{-2 - 2 - 2}}{10^{-1 - 1 - 1}}\;dm^3 ...Law\;1...Exp \\[5ex] =\dfrac{25 * 10^{-6}}{10^{-3}}\;L \\[5ex] = 25 * 10^{-6 - (-3)}\;L ...Law\;2...Exp \\[5ex] = 25 * 10^{-6 + 3}\; L \\[3ex] = 25 * 10^{-3}\;L \\[5ex] \text{Convert from L to mL} \\[3ex] = 25 * 10^{-3}\;L * \dfrac{.......mL}{.......L} \\[5ex] = 25 * 10^{-3}\;L * \dfrac{1\;mL}{10^{-3}\;L} \\[5ex] = 25\;mL \\[5ex] (d.) \\[3ex] 1\;metric\;ton = 1000\;kg \\[3ex] 0.25\;ton * \dfrac{.......kg}{.......ton} \\[5ex] = 0.25\;ton * \dfrac{1000\;kg}{1\;ton} \\[5ex] = 250\;kg $

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