If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it. - Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka



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 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) $5280\:ft = 1\:mi$
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 ($in^3$) $1\:gal = 231\:in^3$


Metric to Customary Conversions
Measurement Metric Customary Unit Conversion Factor
Length meter (m) foot (ft) $1\:ft = 0.3048\:m$
Length nautical miles kilometer (km) $1\:nautical\;\;mile = 1.852\;km$
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) $1\:L = 0.26417205\:gal$

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 1kg = 2.2lbs, convert 3954lb 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 1kg = 2.2lbs, convert 3954kg 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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