Learn how measurement works, why standard units are essential, how the CGS, FPS, MKS and SI systems differ, and how to convert measurements accurately.
Measurement is the process of comparing an unknown physical quantity with a known standard quantity of the same kind. It allows observations to be expressed clearly and compared accurately.
Key relation: Q = n × u
Here, Q is the physical quantity, n is its numerical value and u is the unit. The quantity remains the same when the unit changes; only the numerical value changes.
For example, if a table is 2 metres long, its length is expressed as a numerical value (2) multiplied by the unit (metre). A larger unit gives a smaller numerical value for the same physical quantity, while a smaller unit gives a larger numerical value.
Different units can lead to confusion in trade, engineering and scientific communication. A common system helps people compare results and share measurements without ambiguity.
| Physical quantity | SI unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Thermodynamic temperature | kelvin | K |
| Electric current | ampere | A |
| Luminous intensity | candela | cd |
| Amount of substance | mole | mol |
SI units are internationally standardised and use decimal prefixes such as kilo-, centi- and milli-, which make many conversions straightforward.
During conversion, the unit and numerical value change, but the physical quantity remains constant. Always convert units carefully and show the steps.
Answer: Any two are the CGS system (centimetre–gram–second) and the FPS system (foot–pound–second). MKS and SI are also systems of units.
Answer: SI is internationally accepted, provides consistent standard units and uses decimal prefixes that make conversions easier. It helps scientists, engineers, businesses and countries communicate measurements clearly.
Solution: 1 N = 1 kg m/s2 = 1000 g × 100 cm/s2 = 105 g cm/s2.
Therefore, 250 N = 250 × 105 = 2.5 × 107 g cm/s2, or 2.5 × 107 dyne.
Solution: 1 L = 10−3 m3, so 1 kg/L = 1000 kg/m3.
Therefore, 1000 kg/L = 1000 × 1000 = 106 kg/m3.
Answer: Foot. It is a unit of length in the FPS system. Metre, kilogram and second are SI units.
Answer: The kilogram (kg).
Answer: The International System of Units (SI).
Answer: It prevents confusion and errors when measurements are communicated between people, countries and scientific communities. It also makes measurements easier to compare.
Answer: Measurement assigns numerical values and units to physical quantities such as length, mass, time and temperature. This allows observations to be compared and scientific relationships to be tested quantitatively.
Answer: A measurement is represented by Q = n × u. For example, 5 m means five times the standard unit metre. The same length could be expressed as 500 cm; the quantity is unchanged although the number and unit differ.
Answer: The floor's actual area remains unchanged, but each stick represents a different unit size. A longer stick covers more space per unit, so fewer units are counted; a shorter stick requires more units.
Answer: The numerical value depends on the unit selected. For a fixed quantity, a larger unit gives a smaller numerical value and a smaller unit gives a larger numerical value.
(a) Measurement compares an unknown quantity with a known standard quantity of the same kind.
(b) The SI unit of mass is the kilogram.
(c) In the CGS system, the unit of length is the centimetre.
(d) 1 km = 1000 m.
(e) The internationally accepted system of units is the SI system.
Answer:
Answer: There may be errors in calculations, confusion in international trade, difficulty comparing measurements and problems sharing technical information. Conversions would be required whenever measurements use different units.
Answer: They must convert both measurements into the same unit. Comparing the numerical values alone would be incorrect because a foot and a metre represent different lengths.
Answer: The same stated measurement could represent different actual lengths. This would cause disputes and errors in trade, construction, engineering and scientific research.
Answer: Kilograms and pounds are different units of mass. Converting lets the shopkeeper and customer agree on the same amount.
Solution: Mass in pounds = 5 × 2.2 = 11 pounds.
Solution: 9 km/h = 9 × (1000 m / 3600 s) = 9000/3600 m/s = 2.5 m/s.
Answer: The numerical value is 8 and the unit is centimetre (cm).