Conversion of Units

People use different units of measurement in the things in which they are engaged. There are times that the units used do not match to a person’s preference or convenience as well as standards in certain processes and applications. Converting those units to an extent that it can be understood directly and applied properly is important. For example, a person who is only familiar with the metric system cannot easily figure out how tall is a tree measuring 25 feet in height. Converting 25 feet to probably in meters will help the person know how tall the tree is.


1.  Metric-to-Metric Conversion


Converting a metric unit to another metric unit is the easiest as compared to the other conversions. Familiarization on the equivalent values of the prefixes is important in metric-to-metric conversion.


Here are the steps:


Step #1: Identify the base unit.

Step #2: Determine the prefixes used and their equivalents.

Step #3: Subtract the prefix exponent of the converted unit from the prefix exponent of the original unit.

Step #4: Move the decimal place of the original measurement according to the value of the exponent.


• If the difference is positive, move the decimal place to the right.

• If the difference is negative, move the decimal place to the left. Fill in the extra spaces with zeros.


Example 1.1
 25 cm
Explanation:

Step #1: Identify the base unit.

The base unit is meter (m).


Step #2: Determine the prefixes used and their equivalents.

dm means decimeters.

The prefix is deci which is equivalent to `10^(-1)`.

cm means centimeters.

The prefix is centi which is equivalent to `10^(-2)`.


Step #3: Subtract the exponent of the prefix equivalent of the converted unit from the original unit.

The exponent of `10^(-1)` is –1.

The exponent of `10^(-2)` is -2.

–1 – (-2) = 1


Step #4: Move the decimal place of the original measurement according to the value of the exponent.

• If the difference is positive, move the decimal place to the right.

• If the difference is negative, move the decimal place to the left.

Fill the extra spaces with zeros.

The difference 1 is positive.

So move the decimal point by 1 decimal place to the right.

Measurement

Therefore, 2.5 dm = 25 cm

Example 1.2
 0.6 L
Explanation:

Step #1: Identify the base unit.

The base unit is liter (L).


Step #2: Determine the prefixes used and their equivalents.

mL means millliters.

The prefix is milli which is equivalent to `10^(-3)`.

liter is a base unit so it has no prefix which is equivalent to `10^0`.


Step #3: Subtract the exponent of the prefix equivalent of the converted unit from the original unit.

The exponent of `10^(-3)` is –3.

The exponent of `10^0` is 0.

–3 – 0 = –3


Step #4: Move the decimal place of the original measurement according to the value of the exponent.


• If the difference is positive, move the decimal place to the right.

• If the difference is negative, move the decimal place to the left.

Fill the extra spaces with zeros.

The difference –3 is negative.

So move the decimal point by 3 decimal places to the left.

Measurement

Therefore, 600 mL = 0.6 L

Example 1.3
 7000 g
Explanation:

Step #1: Identify the base unit.

The base unit is gram (g).


Step #2: Determine the prefixes used and their equivalents.

kg means kilograms.

The prefix is kilo which is equivalent to `10^3`.

gram is a base unit so it has no prefix which is equivalent to `10^0`.


Step #3: Subtract the exponent of the prefix equivalent of the converted unit from the original unit.

The exponent of `10^3` is 3.

The exponent of `10^0` is 0.

3 – 0 = 3


Step #4: Move the decimal place of the original measurement according to the value of the exponent.


• If the difference is positive, move the decimal place to the right.

• If the difference is negative, move the decimal place to the left.

Fill the extra spaces with zeros.

The difference 3 is positive.

So move the decimal point by 3 decimal places to the right.

Measurement

Therefore, 7 kg = 7000 g


2.   English-to-English Conversion


Conversion involving English units is a bit tricky since relationship between two English units differ from each other. Familiarization of the conversion table between English units is important in English-to-English conversion.


Here are the steps:


Step #1: Identify the units used.

Step #2: Determine the relationship between the units.

Step #3: Determine the conversion factor (in fraction form).

The denominator should have the same unit as the original measurement.

Step #4: Multiply the original measurement by the conversion factor.


Example 2.1
 2.5 ft
Explanation:

Step #1: Identify the units used.

The units are inches (in) and feet (ft).


Step #2: Determine the relationship between the units.

12 in = 1 ft


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in inches.

So, the denominator of the conversion ratio should be in inches.

The conversion factor is `(1 ft)/(12text( in))`


Step #4: Multiply the original measurement by the conversion factor.

`30text( in) ` x `(1 ft)/(12text( in))` = `2.5 ft`

Therefore, 30 in = 2.5 ft

Example 2.2
 8 qt
Explanation:

Step #1: Identify the units used.

The units are pints (pt) and quarts (qt)


Step #2: Determine the relationship between the units.

1 qt = 2 pt


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in pints.

So, the denominator of the conversion ratio should be in pints.

The conversion factor is `(1 qt)/(2 pt)`


Step #4: Multiply the original measurement by the conversion factor.

`16 pt` x `(1 qt)/(2 pt)` = `8 qt`

Therefore, 16 pt = 8 qt

Example 2.3
 80 fl oz
Explanation:

Step #1: Identify the units used.

The units are pounds (lb) and fluid ounces (fl oz).


Step #2: Determine the relationship between the units.

1 lb = 16 fl oz


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in pounds.

So, the denominator of the conversion ratio should be in pounds.

The conversion factor is `(16 fl oz)/(1 lb)`


Step #4: Multiply the original measurement by the conversion factor.

`5 lb` x `(16 fl oz)/(1 lb)` = `80 fl oz`

Therefore, 5 lb = 80 fl oz

Example 2.4
 1.5 sq. mi
Explanation:

Step #1: Identify the units used.

The units are acres and square miles (sq. mi).


Step #2: Determine the relationship between the units.

1 sq. mi = 640 acres


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in acres.

So, the denominator of the conversion ratio should be in acres.

The conversion factor is `(1 sq. mi)/(640 acres)`


Step #4: Multiply the original measurement by the conversion factor.

`960 acres ` x `(1 sq. mi)/(640 acres)` = `1.5 sq. mi`

Therefore, 960 acres = 1.5 sq. mi


3.  English-to-Metric Conversion and Metric-to-English Conversion


Similar to English-to-English conversion, English-to-Metric and Metric-to-English conversions require familiarization of the conversion table. The relationship between a metric and an English unit is mostly in decimal form, thus great attention to digits is a must in order to prevent conversion errors.


Below is a conversion table between some English and Metric units:


Length
1 in = 2.54 cm
1 ft = 30.48 cm
1 yd = 0.9144 m
1 mi = 1.609 km
Mass
1 kg = 2.2 lbs
1 oz = 28.35 g
Volume
1 gal = 3.785 L

Ares
1 ha = 2.47 acres

The method of english-to-metric and metric-to-english conversion is similar to the english-to-english conversion.


Here are the steps:


Step #1: Identify the units used.

Step #2: Determine the relationship between the units.

Step #3: Determine the conversion factor (in fraction form).

The denominator should have the same unit as the original measurement.

Step #4: Multiply the original measurement by the conversion factor.


Example 3.1
 91.44 cm
Explanation:

Step #1: Identify the units used.

The units are feet (ft) and centimeters (cm).


Step #2: Determine the relationship between the units.

1 ft = 30.48 cm


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in feet.

So, the denominator of the conversion ratio should be in feet.

The conversion factor is `(30.48 cm)/(1 ft)`


Step #4: Multiply the original measurement by the conversion factor.

`3 ft` x `(30.48 cm)/(1 ft)` = `91.44 cm`

Therefore, 3 ft = = 91.44 cm

Example 3.2
 99 lbs
Explanation:

Step #1: Identify the units used.

The units are kilograms (kg) and pounds (lb).


Step #2: Determine the relationship between the units.

1 kg = 2.2 lbs


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in kilograms.

So, the denominator of the conversion ratio should be in kilograms.

The conversion factor is `(2.2 lbs)/(1 kg)`


Step #4: Multiply the original measurement by the conversion factor.

`45 kg` x `(2.2 lbs)/(1 kg)` = `99 lbs`

Therefore, 45 kg = 99 lbs

Example 3.3
 15.14 L
Explanation:

Step #1: Identify the units used.

The units are gallons (gal) and liters (L).


Step #2: Determine the relationship between the units.

1 gal = 3.785 L


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in gallons.

So, the denominator of the conversion ratio should be in gallons.

The conversion factor is `(3.785 L)/(1 gal)`


Step #4: Multiply the original measurement by the conversion factor.

`4 gal` x `(3.785 L)/(1 gal)` = `15.14 L`

Therefore, 45 kg = 15.14 L

Example 3.4
 12.35 acres
Explanation:

Step #1: Identify the units used.

The units are hectares (ha) and acres.


Step #2: Determine the relationship between the units.

1 ha = 2.47 acres


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

The original measurement is in hectares.

So, the denominator of the conversion ratio should be in hectares.

The conversion factor is `(2.47 acres)/(1 ha)`


Step #4: Multiply the original measurement by the conversion factor.

`5 ha` x`(2.47 acres)/(1 ha)` = `12.35 acres`

Therefore, 5 ha = 12.35 acres







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