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Conversion Between Metric Systems and Customary Systems

Samuel Dominic Chukwuemeka (SamDom For Peace) For ACT Students
The ACT is a timed exam...$60$ questions for $60$ minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no "negative" penalty for any wrong answer.

For JAMB and CMAT Students
Calculators are not allowed. So, the questions are solved in a way that does not require a calculator.

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 $10^{24}$


Customary to Customary Conversions
Quantity 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) $5280\:ft = 1\:mi$
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 ($in^3$) $1\:gal = 231\:in^3$


Metric to Customary Conversions
Measurement Metric Customary Unit Conversion Factor
Length meter (m) foot (ft) $1\:ft = 0.3048\:m$
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) $1\:L = 0.264\:gal$

Solve all questions.
Use at least two methods as applicable.
State the measurement.
Show all work.


NOTE: Unless specified otherwise:
(1.) Use only the tables provided for you.
(2.) Please do not approximate intermediate calculations.
(3.) Please do not approximate final calculations. Leave your final answer "as is".

(1.) Using the conversion rate of $1\:kg = 2.2\:lbs$, convert $3954\:lb$ to $kg$


Measurement is Mass

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 3954\:lb\:\:to\:\:kg \\[3ex] 3954\:lb * \dfrac{.....kg}{.....lb} \\[5ex] 3954\:lb * \dfrac{1\:kg}{2.2\:lb} \\[5ex] = 1797.27273\:kg \\[3ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] $
$lb$ $kg$
$2.2$ $1$
$3954$ $x$

$ \dfrac{2.2}{3954} = \dfrac{1}{x} \\[5ex] Cross\:\:Multiply \\[3ex] 2.2 * x = 3954 \\[3ex] x = \dfrac{3954}{2.2} \\[5ex] x = 1797.27273\:kg $
(2.) Using the conversion rate of $1\:kg = 2.2\:lbs$, convert $3954\:kg$ to $lb$


Measurement is Mass

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 3954\:kg\:\:to\:\:lb \\[3ex] 3954\:kg * \dfrac{.....lb}{.....kg} \\[5ex] 3954\:kg * \dfrac{2.2\:lb}{1\:kg} \\[5ex] = 8698.8\:lb \\[3ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] $
$lb$ $kg$
$2.2$ $1$
$x$ $3954$

$ \dfrac{2.2}{x} = \dfrac{1}{3954} \\[5ex] Cross\:\:Multiply \\[3ex] 1 * x = 3954(2.2) \\[3ex] x = 8698.8\:lb $
(3.) Convert $3954$ pounds to kilograms


Measurement is Mass

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 3954\:lb\:\:to\:\:kg \\[3ex] 3954\:lb * \dfrac{.....kg}{.....lb} \\[5ex] 3954\:lb * \dfrac{0.45359237\:kg}{1\:lb} \\[5ex] = 1793.50423\:kg \\[3ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] $
$lb$ $kg$
$1$ $0.45359237$
$3954$ $x$

$ \dfrac{1}{3954} = \dfrac{0.45359237}{x} \\[5ex] Cross\:\:Multiply \\[3ex] 1 * x = 3954(0.45359237) \\[3ex] x = 1793.50423\:kg $
(4.) Convert $3954$ kilograms to pounds


Measurement is Mass

$ \underline{First\:\:Method:\:\:Unity\:\:Fraction\:\:Method} \\[3ex] 3954\:kg\:\:to\:\:lb \\[3ex] 3954\:kg * \dfrac{.....lb}{.....kg} \\[5ex] 3954\:lb * \dfrac{1\:lb}{0.45359237\:kg} \\[5ex] = 8717.07785\:lb \\[3ex] \underline{Second\:\:Method:\:\:Proportional\:\:Reasoning\:\:Method} \\[3ex] $
$lb$ $kg$
$1$ $0.45359237$
$x$ $3954$

$ \dfrac{1}{x} = \dfrac{0.45359237}{3954} \\[5ex] OR \\[3ex] \dfrac{x}{1} = \dfrac{3954}{0.45359237} \\[5ex] x = 8717.07785\:lb $




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