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Measurement
The word measurement is derived from the Greek word 'metron', which translates to "limited proportion". It is one of the most commonly used mathematical terms in daily life. In the article, we will learn more about measurement.
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What is Measurement in Math?
Measurement is defined to describe the comparison between an unknown quantity and a known quantity with standard units. It is one of the fundamental building blocks of mathematics that holds great importance, as it allows us to compare and calculate height, length, width, and numerous other physical quantities.
They are represented with certain units for example, meters, kilos, pounds, minutes, seconds, and many more.
History of Measurement
The earliest recorded sources of measurement goes back to Ancient Egypt.
- In the early 3000 BCE, the Egyptians used measurement as a technique to build pyramids and other structures. They coined the term "cubit" (the length of the forearm). It was built out of a black granite rod, which they even used to measure ropes and rocks.
- Later, in approximately 2500 BCE, the Babylonians developed the earliest unitary system for length and weight. After the Babylonians, around 500 BCE, the Romans created a system of measurement based on the distance covered on foot by the soldiers, which was also adapted by the Egyptians.
- However, none of these were standard measurement units that were followed globally. The real evolution in the field of measurement came when France introduced the metric system in 1795.
- The metric system, introduced by France, was widely adopted by many other European countries, marking a significant step forward in the evolution of standardized measurement.
- The next step in the evolution of measurement and standardizing units for global acceptance occurred in 1960, when the SI system of units was introduced. Since then, there have been more developments that have enhanced the quality of measurement we experience today.
- The developed version of SI unit is the metric system. Today, most of the countries follow SI except some countries like the US, Liberia, and Myanmar.
Measurement Units
Have you ever heard words like meters, liters, grams, feet, inches, pounds, etc.? These are called the units of measurement. They are used to refer physical quantities such as length, weight, volume, etc. Now let’s understand the differences between standard units and non-standard units.
|
Standard Units |
Non-Standard Units |
|
Universally accepted |
Not universally accepted. |
|
Consistent measuring units. |
Measuring units may vary. |
|
Easy to convert from one unit to another. |
They cannot be converted from one unit to another. |
|
Examples: Meters, kilometers, seconds, kelvin, etc. |
Examples: Hand span, arm span, cubit, foot span, pace, and finger width. |
Types of Measurement
Different units and devices are used to measure different objects. The units and devices depend upon the physical properties of the object. A few types of measurement are mentioned below.
- Length Measurement: The distance between two points is called its length. Kilometer, meter, feet, inches, and so on are the units of length.
- Weight/Mass Measurement: Weight is the force exerted on an object due to gravity. The units of weight are grams, kilograms, pounds, tons, etc.
- Time Measurement: Time is measured in seconds, minutes, hours, weeks, months, and years. Time is about the period of an event, which can be past, present, or future.
- Volume Measurement: Volume is the amount of space occupied by a three-dimensional object. The units used are liter, milliliter, quart, and gallon.
- Temperature Measurement: The amount of hotness or coldness of any object is the temperature. We usually measure temperature in either Celsius or Fahrenheit.
- Area Measurement: The space occupied by an object in a two-dimensional space is the area. Area is measured in square units. Like square centimeters (cm2), square meters (m2), and square kilometers (km2).
- Angle Measurement: Angle measurement is a process where we find the size of rotation, which is formed when two rays or lines meet at a common point. The units are degrees and radians.
Measurement Instruments
The accurate measurement of physical quantities such as weight, angle, and force is almost impossible without the use of instruments. There are specific instruments designed to measure particular physical quantities.
- Measurement Tape: Measurement tape is the instrument used to measure the length. Units such as millimeters, centimeters, meters, inches, etc., are usually present on the tape depending upon its type.
- Pendulum Clock: Time is measured using instruments such as clocks, watches, and pendulums. The units of time are seconds, minutes, hours, days, months, etc. Some of the examples of time measurement instruments used from ancient time to present days can be seen in the following image.
- Weight Machine: Weighing machines are used to measure the weight of an object. Weighing machines can be analog or digital. The units for measuring weight are kilograms, grams, milligrams, etc. The following images show some of the instruments used for measuring weight.
Measurement Conversion Formulas
Measurement is incomplete without units. Since units decide the final value of a quantity, it is important to use correct units. For example, it is possible for a single, physical quantity like length to exist in two unitary forms, m and cm. To avoid discrepancies between units and measurement, it is advised to convert all the measurements into a common unit and then solve the problem. Some basic unit conversions are mentioned below.
| Length | Weight | Capacity |
|
\(10 \space mm = 1 \space cm\)
|
\(10 \space mg = 1 \space cg\)
|
\(1 \space mL = 1 \space cL\)
|
Units of Measurement
Earlier, measurements were not accurate, since they used the human body, stones, and seeds to measure. The lack of standardized units usually led to measurement errors. To avoid such errors, we use standard forms of measurement, such as the metric system and the US standard system (Imperial system).
|
Metric System |
Imperial System |
|
Standardized measurement used worldwide. |
The standardized system used mainly in the US. |
|
Easy for conversion as it is based on the powers of 10. |
Requires memorizing the conversion rates. |
|
Units: Kilometers, kilograms, and liters. |
Units: Inches, ounces, and cups. |
Measurement Chart
We use different units of measurements for each physical quantity. For an easier understanding of units of measurement in the two systems, you can refer to the measurement chart.
For metric system
|
Physical Quantities |
Units |
Abbreviation |
|
Length |
Millimeter |
mm |
|
Weight |
Milligrams |
mg |
| Capacity |
Milliliters |
ml |
For the US standard system
|
Physical Quantities |
Units |
Abbreviation |
|
Length |
Inches |
inch |
|
Weight |
Ounces |
oz |
|
Capacity |
Fluid ounce |
fl oz |
The conversion formulas for metric to US standard system and vice versa can be obtained from the following chart:
Basic Rules and Properties of Measurement
When measuring any object, we need to follow certain rules. Some basic rules and properties of measurement are:
- Consistency: While measuring an object multiples times, there should be no variation in the measure of the object's physical quantity.
- Accuracy and Precision: The measurement of any object should be precise or as close to precise as possible for better results. Accuracy of measurement depends on method used too, so the correct methods and instruments should be used for precise and accurate measurement.
- Estimation: Estimation is making an approximate value for an object when there is a limitation.
- Standardization: Standardization refers to the use of universally recognized units for measurement.
Begin your journey into the realm of measurement by exploring the key concepts listed below:
Tips and Tricks to Master Measurement
Whenever we measure, the measurement should be accurate and precise. As we have learned all about measurements now, let's see some tips and tricks to master measurement.
- Understanding basic units: Students should try to learn and memorize the basic standardized units of measurement.
- Using measuring tools effectively: For each physical quantity, we have different measuring tools. So, when measuring, try to use the correct measurement tools.
- Converting units at the start of calculation: Units should be converted at the start of calculations to avoid confusions and discrepancies in measurement. Similar units of the same measurement system give accurate and precise answers.
- Converting between units: It is important to be extremely careful when converting units, as units decide the final value of the solution. Applying the wrong units and using incorrect formula can lead to wrong answers.
- Be careful while adding units to the final values: After measurement or calculations, it is crucial to apply the correct units at the end because a particular unit defines certain physical quantities. For example, if the unit radian is applied in place of degree, it changes the entire value of the measured quantity.
Common Mistakes and How to Avoid Them in Measurement
Learning measurement is essential to know about volume, area, shapes, angles, and many other branches of math. So, for a better understanding, let’s check out some common mistakes in measurements and ways to avoid them.
Mistake 1
Mistakes while converting units
Errors are common when converting units from one to another. To avoid such mistakes, we need to remember certain basics of conversion. For example, when doing unit conversion in a metric system, we need to either multiply or divide the value with powers of 10.
Mistake 2
Confusion with units
For each of the physical quantities, there are different measurement units. Hence, it's common among students to get confused with the units. To avoid this mistake, students should understand the relationship between units.
Mistake 3
Errors in calculation
Due to carelessness and lack of practice, students tend to make basic calculation errors. So, always double-check and verify the answer when converting from one unit to another.
Mistake 4
Using the wrong tools for measurement
Using the wrong tools for measurements leads to wrong answers.
For example, if we use a simple ruler to measure the length of a screw instead of a vernier’s caliper, the value shown will be inaccurate.
Mistake 5
Using the right instruments incorrectly to measure a quantity
Certain measuring tools have a particular method and steps that need to be followed to achieve precise and accurate results.
For example, while calculating time as a quantity using pendulum, the oscillations have to be observed at regular time intervals that are pre-decided. If the time interval between certain oscillations is wrongly measured, it could lead to wrong answers.
Hence, it is important to use the right instruments with the correct set of instructions.
Real-World Applications of Measurement
Measurement is all around us. We use it in the fields of construction, cooking, sports, and so on. Let’s explore how we use measurement in the real world.
- Construction: In the field of construction, we need accurate measurements of the length, width, and height of the building.
For example, building a house of height 12 feet.
- Sports: In sports, we use measurement to measure the field of play, performance of athletes, number of players, scores, etc.
For example, a football team has a total of 11 players.
- Cooking: While cooking, we use units to measure the amount of ingredients.
For example, adding 2 ml of vanilla essence.
- Traveling: While traveling from destination A to B, the distance between the two is measured to calculate the ETA.
For example, the distance from New York to LA is 3974 km.
- Medicinal Purposes: Dosages of medicines need to be measured precisely before they are administered to the patients.
For example, WHO recommends 70 and 100 mg/dL of fasting glucose (varies).
Solved Examples in Measurements
Problem 1
Tom wants to tile his garden, the length of each side of the square garden is 5200 mm. The cost of tiling 1 square meter of the garden is $2. How much is the total cost?
The total cost for tiling the garden is $54.08.
Explanation
Given:
- The length of the garden = 5200 mm
- Cost of tiles per square meter = $2
- Length of the garden in meter = \(5200 ÷ 1000 = 5.2 m\)
Area of the garden = \(s^2 = (5.2)^2 = 27.04 m^2\)
Total cost = \(27.04 × 2 = $54.08\)
Problem 2
Harry needs 5 kg of flour, but in the shop, they only sell flour in packets of 200 grams. Calculate how many packets of flour Harry needs to buy.
The total number of flour packets that Harry needs to buy is 25.
Explanation
Given:
- Total flour needed = 5 kg
- The weight of flour in each packet = 200g
Since, \(1kg = 1000g\)
Total flour Harry needs in grams \(= 5 × 1000 = 5000 g\)
Number of packets required \(= 5000 ÷ 200 = 25\)
Harry needs to buy 25 packets of flour.
Problem 3
The dimensions of a room are 10 ft, 22 ft, and 34 ft. Find the volume of the room.
The volume of the room is 7,480 ft3.
Explanation
Given:
- Volume of rectangular room \(= L × W × H\)
- Here, \( L = 34 \space \text ft\)
- \(W = 22 \space \text {ft}\)
- \(H= 10 \space \text {ft}\)
Volume \(= 34 × 22 × 10 = 7480 ft^3\)
Therefore, the volume is 7480 ft3.
Problem 4
A boy’s height is 165 cm. Express the height in meters.
1.65 meters.
Explanation
To convert the height from centimeters to meters, we divide it by 100 because 1 meter is 100 centimeters.
So, 165 centimeters in meters \(= {165 \over {100}} = 1.65 \space \text {meters}\)
Problem 5
The area of a square park is 64 m². Calculate its perimeter.
32 meters.
Explanation
The formula for area of a square is side2
Therefore,
Side \(= { \sqrt{area} }\)
Side \(= {\sqrt{64} }\)
Side \(= 8 \space m\)
Now, the perimeter of square \(= 4 × side\)
Perimeter \(= 4 × 8 \)
Perimeter \(= 32 \space m\)
FAQs on Measurements
1.What are the seven basic units of measurement that my child needs to know?
2.What are the three types of measurement that children should know?
3.How can my child measure time?
4.Which symbol can by child use to represent foot?
5.Why is measurement important for my child?
6.Mention five uses of measurement for children.
7.What are the functions of measurement that my child should know?
8.Mention the two properties of measurement that children should learn?
9.Mention three things that my child measure in everyday life.
Explore More Math Topics
From Numbers to Geometry and beyond, you can explore all the important Math topics by selecting from the list below:
| Numbers | Multiplication Tables |
| Geometry | Algebra |
| Calculus | Trigonometry |
| Commercial Math | Data |
| Math Formulas | Math Questions |
| Math Calculators | Math Worksheets |
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
