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Measurement

Measurement is an important topic in mathematics and many other fields. It is used in engineering, construction, medicine, cooking, and other fields. Let’s learn more about measurement and its features.

Foundational
Intermediate
Advance Topics
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What is Measurement in Math?

The way of expressing the quantity of an object in numbers with units is known as measurement. Measurement involves determining the weight, height, volume, etc, of an object. Measurements are represented by certain units like meters, kilos, pounds, gallons, celsius, minutes, and so on.

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History of Measurement

When learning measurement, it is important to learn about how it all began. In ancient times, lengths were measured based on the human body. For e.g., they used the width of their thumb and length of their foot to measure things.     

Around 3000 BC, the Egyptian cubit was widely accepted as the standardized measuring unit. Based on the existing measuring idea, a standard royal cubit was used. The cubit was a black granite rod whose length was the same as the length of a royally-assigned arm.  

Harappan civilisation thrived in South Asia between 2500 and 1700 BC. Recent excavations at present-day Pakistan have proved that the Harappans had a uniform system of measures. Europeans, on the other hand, had adopted the Roman measuring system, which was originally based on those of Greece. 

When trade, industries, and travel expanded worldwide, a need for standardized measurement came. The need was intensified during the French Revolution, leading to the formation of the International System of Units (SI unit). The developed version of the SI unit is the metric system. Today, most countries follow the metric system while some countries like the US use the imperial system, also known as the US Standard system.
 

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Measurement Units

Have you heard words like meters, liters, grams, feet, inches, pounds, etc? These are the units of measurement. These 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 and consistent measuring units
  • Easy to convert from one unit to another
  • Meters, kilometers, seconds, kelvin, and so on are the standard units
  • Not universally accepted. Measuring units may vary
  • It cannot be converted from one unit to another
  • Hand span, arm span, cubit, foot span, pace, and finger width are the non-standard units

 

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Types of Measurement

We use different units and devices based on the physical qualities of an object. Weight, volume, length, time, temperature, area, and angle There are different physical qualities like.
 

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Length Measurement

The distance between two points is what we call length. Kilometer, meter, feet, inches, and so on are the units of length. 
 

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Weight/Mass Measurement

Weight is the heaviness of an object as compared to the other. The units are grams, kilograms, pounds, tons, etc. 
 

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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. 

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Volume Measurement

Volume is the amount of substance a three-dimensional object can hold. The units used are liter, milliliter, quart, and gallon.

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Temperature Measurement

The amount of hotness or coldness of any object is the temperature. We usually measure temperature, commonly in either Celsius or Fahrenheit.
 

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Area Measurement

The space occupied by an object in a two-dimensional space is the area. Square units are the unit of measurement of area. Like square centimeters (cm2), square meters (m2), and square kilometers (km2).

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Angle Measurement

The angle formed between two rays is the angle measurement. The units are degrees and radians.

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Measurement Instruments

Measurement instruments are the tools used to measure physical qualities of any object. They make our lives easy as they help us know accurate measurements of anything that needs to be measured. For e.g., a scale marked with graduations can be used to draw multiple parallel lines with equal spacing between each lines. For different objects based on their properties, different tools are used. So let’s see some commonly used measurement instruments.
 

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Measurement Tape

Measurement tape is the instrument used to measure the length. Millimeters, centimeters, meters, inches, etc. are the units.
 

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Pendulum Clock

The instrument used to measure time is a clock. The units are seconds, minutes, hours, days, months, etc.
 

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Weight Machine

It is the instrument used to measure the weight of any object. Weight machines can be manual or digital.
 

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Measurement Conversion Formulas

Now we have learned about different types of measurements and units of measurement. All the measurement units are interconnected. 

Measurement conversion is the process of converting a unit from one to another. 
For example, 1 kg can be converted to 1000 g. Here we are going to learn more about measurement conversions in the metric system.

The metric system is based on the power of 10. That means, to convert from one unit to another, we will multiply or divide the value by 10.

Length Weight Capacity
10 mm = 1 cm
100 cm = 1 m
1000 m = 1 km

10 mg = 1 cg
100 cg = 1g
1000 g = 1 kg

10mL = 1 cL
100cL = 1 L
1000 L = 1 Kl

 

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Units of measurement

Earlier, measurements were not accurate, as they used the human body, stones, and seeds to measure and there were no standardized units. This usually led to measurement errors. To avoid such errors, we use a standard form of measurement, which is known as the metric system and the US standard system (Imperial system). 
 

 

Metric system

Imperial System

  • Standardized measurement used worldwide
  • Easy for conversion as it is based on the powers of 10
  • Units: Kilometers, kilograms, and liters. 
  • The standardized system used mainly in the US 
  • Needs to memorize the conversion rates
  • Units: Inches, ounces, and cups 

 

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Measurement chart

For each physical quality, we have different units of measurement. For an easier understanding of units of measurement in the two systems, you can refer to the measurement chart.

For metric system

Physical qualities

Units

Abbreviation

Length

Millimeter
Centimeter
Meters
Kilometers

mm
Cm
m
km

Weight

Milligrams
centigrams
Grams
Kilograms

Mg
cg
g
kg

Capacity

Milliliters
Centiliter
Liters
kiloliter

Ml
cl
l
Kl


For the US Standard system

Physical qualities

Units

Abbreviation

Length

Inches
Feet
Yards
miles

inch
ft
yd
mi

Weight

Ounces
Pounds
Ton

oz
lbs
t

Capacity

Fluid ounce
Cup
Pint
Quarts
Gallon 

fl oz
c
pt
qt
gal


 

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Basic Rules and Properties of Measurement

The fundamental concept of physics, math, engineering, etc. is measurement. So when measuring any object, we need to follow certain rules. Some basic rules and properties of measurement are

 

Consistency: The value of measurement of an object should be the same, even if you measure it multiple times. 

Accuracy and Precision: The closeness of a measured value to the true value is accuracy. Whereas, the consistency of obtaining the same result when measuring the same object multiple times is precision.

Estimation: Estimation is making an approximate value for an object when there is a limitation. 

Standardization: Standardization refers to the use of a universally recognized unit for measuring.  
 

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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 quality, we have different measuring tools. When measuring try to use the correct measurement tool, and do the basic check before measuring.

 

Converting between units

As we know, metric system is based on the power of 10. So, when converting from one unit to another, we either divide or multiply it by 10. 

 For example, 1 km = 1000 m, so to convert from km to m we multiply it by 1000. That is 5 km = 5000 m. 


 

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Common Mistakes and How to Avoid Them in Measurement

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Real-World Application of Measurement

Measurement is all around us, we use it in the field 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

Sports: In sports, we use measurement field measurement, the performance of the athlete, and progress 

Cooking: While cooking, we need to measure the ingredients 
 

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Solved examples in measurements

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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 dollars. Then how much is the total cost?

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Explanation

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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.

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Explanation

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Problem 3

The dimensions of a room are 10 ft, 22 ft, and 34 ft. Then find the volume of the room

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Explanation

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FAQs on Measurements

1.What are the seven basic units of measurement?

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2.What are the three types of measurement?

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3.Is time an interval or a ratio?

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4.What is the symbol of the foot?

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