Fundamental and Derived Units of Measurement

Fundamental units are the basic units of measurement defined by the International System of Units (SI). They include the meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.

Derived units are units that are expressed in terms of fundamental units. For example, the unit of velocity, meter per second (m/s), is derived from the fundamental units of meter and second.

The choice of fundamental units is based on their simplicity, universality, and independence from any particular system of measurement.

Derived units are created by combining fundamental units using mathematical operations such as multiplication, division, and exponentiation.

The use of fundamental and derived units allows for a consistent and standardized system of measurement across different fields of science and technology.

History of measurement

History of Measurement

The history of measurement is a long and fascinating one, dating back to the earliest civilizations. As humans began to trade and build, they needed ways to measure distances, weights, and volumes. Over time, a variety of measurement systems developed, each with its own unique advantages and disadvantages.

Ancient Measurement Systems

Some of the earliest measurement systems were based on the human body. For example, the ancient Egyptians used the length of a man’s forearm as a unit of measurement, while the ancient Greeks used the length of a man’s foot. Other measurement systems were based on natural phenomena, such as the movement of the sun or the phases of the moon.

As civilizations grew and became more complex, the need for more accurate and standardized measurement systems became apparent. In the 13th century, the English government established a system of weights and measures that was based on the Tower of London. This system was later adopted by other countries, and it eventually became the basis for the modern metric system.

The Metric System

The metric system is a decimal system of measurement that is based on the meter, the kilogram, and the second. It is the most widely used measurement system in the world, and it is used in all scientific research. The metric system is also used in many countries for everyday measurements, such as measuring the length of a room or the weight of a person.

The Future of Measurement

The future of measurement is likely to see continued advances in accuracy and precision. New technologies, such as lasers and atomic clocks, are making it possible to measure distances and time with unprecedented accuracy. These advances are opening up new possibilities for scientific research and technological development.

Examples of Measurement in Everyday Life

We use measurement in all aspects of our everyday lives. Here are a few examples:

• When we cook, we measure the ingredients in a recipe.
• When we build a house, we measure the dimensions of the materials we need.
• When we drive a car, we measure the speed at which we are traveling.
• When we go to the doctor, our blood pressure and temperature are measured.

Measurement is essential for our everyday lives. It allows us to communicate with each other accurately, to build things that work, and to stay safe.

The Seven Base Units of Measurement

Frequently Asked Questions – FAQs

What is measurement?

Measurement is the process of assigning numbers to objects or events according to a rule. The numbers assigned are called measurements, and they can be used to compare the objects or events. For example, we can measure the length of a table by assigning a number to it, such as 100 centimeters. This number tells us how long the table is compared to a standard unit of length, such as the centimeter.

There are many different types of measurements, and each type has its own set of rules. Some common types of measurements include:

• Length: The distance between two points.
• Mass: The amount of matter in an object.
• Volume: The amount of space an object takes up.
• Temperature: The degree of hotness or coldness of an object.
• Time: The duration of an event.

Measurements are essential for science because they allow us to quantify the world around us. By measuring things, we can learn more about them and how they work. For example, by measuring the length of a table, we can learn how much space it will take up in a room. By measuring the mass of an object, we can learn how much it weighs. By measuring the volume of a liquid, we can learn how much of it there is.

Measurements are also used in everyday life. For example, we use measurements to cook, to build things, and to travel. When we cook, we measure the ingredients we use so that we can make the recipe correctly. When we build things, we measure the materials we use so that they fit together properly. When we travel, we measure the distance we travel so that we know how far we have to go.

Measurement is a fundamental part of our world, and it plays an important role in both science and everyday life.

Define a unit.

A unit is a standard quantity of measurement used to express the magnitude of a physical property. It provides a reference point for comparing and quantifying different measurements. Units are essential in science, engineering, and everyday life, allowing us to communicate and understand measurements accurately.

Here are some key points about units:

1. Standard and Consistency: Units are standardized to ensure consistency and comparability of measurements across different regions, countries, and scientific disciplines. Standardization bodies, such as the International System of Units (SI), establish and maintain these standards.

2. Base and Derived Units: The SI defines seven base units that form the foundation of the system. These include the meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for the amount of substance, and candela (cd) for luminous intensity.

3. Derived Units: Derived units are expressed in terms of combinations of base units. For example, velocity is derived from length and time, and is expressed in units of meters per second (m/s).

4. Dimensional Analysis: Units play a crucial role in dimensional analysis, which involves checking the consistency of units in equations and calculations. This ensures that the units on both sides of an equation match, preventing errors and ensuring the validity of the results.

5. Unit Conversion: Units can be converted from one system to another using conversion factors. For instance, to convert from kilometers (km) to miles (mi), we can use the conversion factor 1 mi ≈ 1.609 km.

6. Uncertainty and Precision: Units are also associated with uncertainty and precision. Uncertainty refers to the range within which the true value of a measurement is likely to fall, while precision indicates the closeness of repeated measurements to each other.

Examples of units in different contexts:

• Length: Meter (m), centimeter (cm), kilometer (km), inch (in), foot (ft), mile (mi)
• Mass: Kilogram (kg), gram (g), pound (lb), ounce (oz)
• Time: Second (s), minute (min), hour (h), day (d), year (yr)
• Temperature: Kelvin (K), degree Celsius (°C), degree Fahrenheit (°F)
• Volume: Liter (L), milliliter (mL), gallon (gal), quart (qt)
• Speed: Meters per second (m/s), kilometers per hour (km/h), miles per hour (mph)

Units are fundamental to scientific communication and understanding. They enable us to quantify, compare, and analyze physical properties accurately and consistently, facilitating progress in various fields of science, technology, and everyday life.

What are significant figures ?

Significant Figures

In science, measurements are never exact. There is always some degree of uncertainty associated with every measurement. The number of significant figures in a measurement indicates the level of precision of that measurement.

Rules for Determining Significant Figures

1. All nonzero digits are significant.
2. Zeros between nonzero digits are significant.
3. Zeros at the end of a number are significant if there is a decimal point.
4. Zeros at the end of a number are not significant if there is no decimal point.

Examples

• 123.4 has four significant figures.
• 0.00123 has three significant figures.
• 100 has two significant figures.
• 100.0 has three significant figures.
• 1000 has one significant figure.

Rounding Significant Figures

When rounding a number to a certain number of significant figures, the following rules apply:

• If the digit to be dropped is less than 5, the last remaining digit is unchanged.
• If the digit to be dropped is greater than 5, the last remaining digit is increased by 1.
• If the digit to be dropped is 5, the last remaining digit is unchanged if it is even and increased by 1 if it is odd.

Examples

• 123.45 rounded to two significant figures is 120.
• 0.001234 rounded to three significant figures is 0.00123.
• 100.5 rounded to two significant figures is 100.
• 100.4 rounded to two significant figures is 100.

Significant Figures in Calculations

When performing calculations with numbers that have different numbers of significant figures, the answer should be rounded to the same number of significant figures as the number with the fewest significant figures.

Examples

• 123.4 + 56.78 = 180.2
• 123.4 - 56.78 = 66.62
• 123.4 * 56.78 = 7024.152
• 123.4 / 56.78 = 2.173

Conclusion

Significant figures are an important part of science. They allow us to communicate the level of precision of our measurements and to perform calculations with confidence.

Define supplementary units.

Supplementary units are units of measurement that are not part of the International System of Units (SI) but are still widely used in specific fields or applications. These units are often based on historical or practical considerations and are accepted for use alongside SI units.

Here are some examples of supplementary units:

1. Time:

   • Minute (min): 1 minute = 60 seconds
   • Hour (h): 1 hour = 60 minutes = 3600 seconds
   • Day: 1 day = 24 hours = 1440 minutes = 86400 seconds

2. Plane angle:

   • Degree (°): 1 degree = 1/360 of a full circle
   • Minute of arc (′): 1 minute of arc = 1/60 of a degree
   • Second of arc (″): 1 second of arc = 1/60 of a minute of arc

3. Solid angle:

   • Steradian (sr): 1 steradian is the solid angle that is subtended at the center of a sphere by a surface area on the sphere equal to the square of the radius of the sphere.

4. Navigation:

   • Knot: 1 knot is equal to one nautical mile per hour.
   • Nautical mile: 1 nautical mile is approximately 1.852 kilometers.

These supplementary units are widely used in various fields such as navigation, astronomy, surveying, and everyday life. While they are not part of the SI system, their usage is recognized and accepted internationally.

How is force measured in a metric system?

In the metric system, force is measured in newtons (N). One newton is the amount of force required to accelerate a one-kilogram mass at a rate of one meter per second squared.

Here are some examples of how force is measured in newtons:

• The force of gravity on a one-kilogram mass is approximately 9.8 newtons.
• The force required to lift a ten-kilogram mass is approximately 98 newtons.
• The force required to push a car with a mass of 1,000 kilograms at a speed of 10 meters per second is approximately 10,000 newtons.

Force can also be measured in other units, such as pounds (lb) or kilograms (kg). However, the newton is the standard unit of force in the metric system.

To measure force in newtons, you can use a device called a force gauge. A force gauge is a spring-loaded device that measures the amount of force applied to it. The force gauge will display the force in newtons.

Force gauges are used in a variety of applications, such as:

• Measuring the force of gravity
• Measuring the force required to lift or move objects
• Measuring the force of a spring
• Measuring the force of a fluid

Force is an important concept in physics. It is used to describe the interaction between objects. Force can be used to explain why objects move, why objects stop moving, and why objects change direction.