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# Measurement Units

## DEFINITION OF MEASUREMENT

Measurement means to describe and compare mathematical and concrete objects using numbers and measurement units. To measure something is to determine how large or small a physical quantity is compared to its reference unit. In mathematics, measurement focuses on properties such as length, mass and weight, time, money, and temperature. Moreover, it is also involved in finding the perimeter, area, surface area, volume, and angle measure.

## WHAT IS MEASUREMENT UNITS?

Measurement units is a standardized quantity used to represent physical quantity. When we say it is a unit of, it simply means there is one of. 1 meter, 1 second, 1 kilogram, etc. are all units.

## SYSTEMS OF MEASUREMENT UNITS

The system of units differs from country to country. These systems are composed of set of rules and units of measurements relating them to each other.

During the ancient times, measurement is usually based on human body and nature. For example, using the thumb, the span of hands and arms, and the foot to measure lengths. More so, ancients based the time by the cast of shadow of the vertical stick and by the movement of sun. The methods used by the ancients were later developed to make a standardized and universal system.

### INTERNATIONAL SYSTEM OF UNITS

The International System of Units, also known as SI Units, is the current globally used metric system. The system was established in 1960 at the General Conference on Weights and Measures.

BASE UNITS

The table below shows the seven base units of the SI Units.

DERIVED UNITS

Derived units are units which can be expressed in terms of base units by means of multiplication and division symbols. The table shows some of the derived SI units.

NON-SI UNITS

Non-SI units are units that is accepted for use with SI. Most of these non-SI units are continuously used every day.

SI PREFIXES

SI prefixes are used to identify multiples or fractions of the base units. The table below shows the SI prefixes, symbol, and multiplicative factor.

### BRITISH IMPERIAL SYSTEM

British Imperial System, also called as Imperial Units, is the official weights and measures system used in Great Britain from 1824 to 1965.

IMPERIAL UNITS FOR LENGTHS

IMPERIAL UNITS FOR AREA

IMPERIAL UNITS FOR LIQUID AND DRY MEASURES

### US CUSTOMARY SYSTEM

The US Customary System Unit is a system of measurement used in the United States and its territories since 1832. Americans use this system in commercial, personal, and social use.

US CUSTOMARY SYSTEM UNITS FOR LENGTHS

US CUSTOMARY SYSTEM FOR DRY VOLUME

US CUSTOMARY SYSTEM FOR LIQUID VOLUME

## LENGTH

### DEFINITION OF LENGTH

Length is an attribute that describes how long a thing is from one end to the other. It is used to identify how long or short think or thick the size of an object or part of an object is. The unit system of length also determines the thickness and thinness of an object.

### CONVERSION OF LENGTHS

CONVERTING LENGTHS IN SI UNITS

To convert length measures given different SI Units, you must:

1. Take note of the SI prefixes and its multiplicative factors.
2. Multiply the given by the multiplicative factor to which you will convert it.
3. Always put the label of measurement.

The table below shows the different measures in lengths and its multiplicative factor.

EXAMPLE #1

Convert 2,867 kilometers to meters.

SOLUTION

Since kilometer is greater than meters, we will multiply the given to its multiplicative factor. Based on the SI prefixes, the multiplicative factor between kilometer and meter is . Thus, we will multiply 2,867 by  or 1000.

$2 867 km \times \frac{1000m}{1km}=2 867 000 m$

Therefore, 2,867 km when converted to meters is 2 867 000 m.

EXAMPLE #2

Convert 821 centimeters to meters.

SOLUTION

To convert centimeters to meters, we will simply divide its multiplicative factor to the given since centimeters is smaller than meters. The multiplicative factor between centimeter and meter is $10^{-2}$ or $\frac{1}{100}$. Hence,

$821cm\times \frac{1m}{100cm}=8.21 m$

Therefore, 821 cm is also equal to 8.21 m.

CONVERTING LENGTHS IN US CUSTOMARY SYSTEM

To convert lengths using the US Customary System, you must:

1. Remember the equivalent measures of certain units.
2. Multiply the given to the conversion factor to which you are going to convert it.
3. Always put the label of measurement.

EXAMPLE #1

How many feet are there in 27 yards?

SOLUTION

To convert yards to feet, simply multiply 27 yards to 3 feet since yards is larger than feet. Hence,

$27 yd \times \frac{3ft}{1yd}=81ft$

Therefore, 27 yards when converted to feet is 81 ft.

EXAMPLE #2

How many feet are there in 30 inches?

SOLUTION

To convert inches to feet, simply multiply 30 inches to 1/12 feet. Thus,

$30 in\times \frac{1ft}{12in}=2.5ft$

Thus, 30 inches is equal to 2.5 feet.

CONVERTING LENGTHS TO US CUSTOMARY SYSTEM AND SI UNIT

The table below shows the equivalent measures of US Customary System to the current Metric System, SI Unit. This table will be helpful in converting lengths from US Customary measures to SI Unit measures, and vice versa.

EXAMPLE #1

Convert 9.3 miles to kilometers.

SOLUTION

To convert 9.3 miles to kilometers, simply multiply 9.3 miles to 1.61km.

$9.3 mi \times \frac{1.61km}{1mi}=14.973$

Therefore, 9.3 miles is equal to 14.973 km.

EXAMPLE #2

What is 400 meters when converted to pica?

SOLUTION

Given the equivalent table for US Customary and SI units, we only have 1 pica = 4.2333 mm. So, we will first convert 4 meters to millimeters.

$4 m \times \frac{1000mm}{1m}=4 000 mm$

Next step is to convert 4000 mm to pica. Since 1 pica = 4.2333 mm, we will put 4.2333 mm to the denominator.

$4 000 mm \times \frac{1pica}{4.2333 mm}=944.889 pica$

Therefore, 4 meters is equal to 944.889 pica.

## MASS AND WEIGHT

### DEFINITION OF WEIGHT

Weight is an attribute that measures how heavy an object is.

### CONVERSION OF WEIGHT

CONVERTING WEIGHTS IN SI UNITS

To convert weight measures given different SI Units, you must:

1. Take note of the SI prefixes and its multiplicative factors.
2. Multiply the given by the multiplicative factor to which you will convert it.
3. Always put the label of measurement.

The table below shows the different measures in lengths and its multiplicative factor.

EXAMPLE

Convert 7 kilograms to milligram.

SOLUTION

To convert 7 kilograms to milligram, we need to convert it first to gram. Thus,

$7kg \times \frac{1000g}{1kg}=7000 g$

Then, convert 7000 grams to milligrams by:

$7000 g \times \frac{1000mg}{1g}=7 000 000 mg$

Therefore, 7 kilograms is the same as 7 000 000 mg

CONVERTING WEIGHTS IN US CUSTOMARY SYSTEM

To convert weights using the US Customary System, you must:

1. Remember the equivalent measures of certain units.
2. Multiply the given to the conversion factor to which you are going to convert it.
3. Always put the label of measurement.

EXAMPLE

What is the equivalent measure of 124 ounces to pounds?

SOLUTION

Since pounds is a greater measure than ounces, we will put the equivalent measure in the denominator of the multiplicative factor. Thus,

$4oz\times \frac{1lb}{16oz}=7.75 lb$

Therefore, 124 oz is equal to 7.75 lb.

CONVERTING WEIGHTS TO US CUSTOMARY SYSTEM AND SI UNIT

The table below shows the equivalent measures of US Customary System to the current Metric System, SI Unit. This table will be helpful in converting weights from US Customary measures to SI Unit measures, and vice versa.

EXAMPLE

Kyle weighs 50 kg, what is his weight if converted into pounds?

SOLUTION

To convert Kyle’s weight into pounds, multiply 50 kg by $\frac{1lb}{0.453kg}$. Thus,

$50kg\times \frac{1lb}{0.453kg}=110.38 lb$

## CAPACITY

### DEFINITION OF CAPACITY

Capacity is the maximum amount of a what a container can hold.

### CONVERTING CAPACITY

CONVERTING CAPACITY IN SI UNITS

To convert capacity measures given different SI Units, you must:

1. Take note of the SI prefixes and its multiplicative factors.
2. Multiply the given by the multiplicative factor to which you will convert it.
3. Always put the label of measurement.

The table below shows the different measures in lengths and its multiplicative factor.

EXAMPLE

Convert 8.3 liters to milliliters.

SOLUTION

To convert 8.3 liters to milliliters, multiply $\frac{1000mL}{1L}$ to 8.3 liters.

$8.3 L\times \frac{1000mL}{1L}=8300 mL$

Thus, 8.3 L is equivalent to 8300 mL.

CONVERTING WEIGHTS IN US CUSTOMARY SYSTEM

To convert weights using the US Customary System, you must:

1. Remember the equivalent measures of certain units.
2. Multiply the given to the conversion factor to which you are going to convert it.
3. Always put the label of measurement.

EXAMPLE

How many ounces are there in 4 pints?

SOLUTION

To find out how many ounces are there in 4 pints, convert 4 pints to cups first. Hence,

$4 pt\times \frac{2c}{1pt}=8c$

Then, convert 8 cups to ounces. Thus,

$8c\times \frac{8oz}{1c}=64 oz$

Therefore, there are 64 oz in 4 pints.

CONVERTING WEIGHTS TO US CUSTOMARY SYSTEM AND SI UNIT

The table below shows the equivalent measures of US Customary System to the current Metric System. This table will be helpful in converting capacity from US Customary measures to SI Unit measures, and vice versa.

EXAMPLE #1

What is 3 gallons when converted to liters?

SOLUTION

To convert 3 gallons to liters, simply multiply 3.785 liters to 3 gallons. Thus,

$3 gal\times \frac{3.785 L}{1 gal}=11.355 L$

Therefore, there are 11.355 L or 11.36 L in 3 gallons.

EXAMPLE #2

Convert 7.5 liters to quarts.

SOLUTION

To convert 7.5 liters to quarts, multiply $\frac{1qt}{0.946 L}$ to 7.5 liters. Thus,

$7.5 L\times \frac{1qt}{0.946 L}=7.928 qt$

Therefore, there are 7.928 quarts or 7.93 quarts in 7.5 liters.

## TIME

### DEFINITION OF TIME

Time is the continuous sequence of events from past, present, and to the future. It is used to measure certain periods during an action, process, or event. We can measure time based on seconds, minutes, hours, days, weeks, and years by using clocks and calendars.

Time – Definition with Examples, digital photograph, SplashLearn, https://www.splashlearn.com/math-vocabulary/time/time. Accessed 23 Sept. 2021.

### CONVERSION OF TIME

The table below shows the standard units of time and its equivalent measures.

In converting time in terms of months to days, the number of days will depend on the corresponding month as it sometimes can be 27 days, 28 days, 30 days, or 31 days. Meanwhile, during leap years, the number of days in a year is 366 days.

EXAMPLE

How many hours are there in 5 days?

SOLUTION

To convert hours to days, simply multiply 24 hours to the number of days. Hence,

$5 d\times \frac{24h}{1d}=120 h$

Therefore, there are 120 hours in 5 days.

## TEMPERATURE

### DEFINITION OF TEMPERATURE

Temperature is an attribute that describes how hot or cold an object or place is. Temperature is measured with the help of thermometer. While the metric system used Kelvin as a standard unit of measurement of temperature, people usually use Celsius (°C) or Fahrenheit (°F) to measure temperature.

### CONVERSION OF TEMPERATURE

The table below shows the different formula in converting temperatures.

EXAMPLE #1

The temperature for today measures 28°C , what is its equivalent in Fahrenheit?

SOLUTION

Using the formula,

Therefore, 28°C is equivalent to 82.4°F.

EXAMPLE #2

What is 500 Kelvin converted to Celsius?

SOLUTION

Using the formula,

℃ = K – 273°

℃ = 500 – 273°

℃ = 227°

Therefore, 500 Kelvin is equal to 227.