SI Units for Plane Angle and Solid Angle

Units and Measurement

• A unit is a standard quantity used to express physical quantities.
• Only a limited number of units are needed to express all physical quantities because they can be combined to express derived quantities.
• The units for fundamental or base quantities are called base units.
• The units obtained for physical quantities that are derived from base units are called derived units.
• A complete set of base and derived units is known as a system of units.

SI System

• The SI system is a widely used system of units that consists of 7 base units.
• The SI unit for plane angle is the radian (rad).
• The SI unit for mass is the kilogram (kg).
• The second is defined in the SI system as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
• The symbol for the SI unit of electric current is the ampere (A).
• The quantity that has a dimensionless unit is the plane angle.

Significant Figures

• The number 0.004700 km has 4 significant figures.
• The best way to remove ambiguities in determining the number of significant figures is to use scientific notation.
• In scientific notation, a number is typically expressed as a × 10^n, where a is between 1 and 10.
• The number of significant figures does not change when changing units in a measurement.
• When rounding off a number in scientific notation, if 'a' is less than or equal to 5, it should be rounded to 0.
• If a number is less than 1, the leading zeros are not considered significant.
• The rule for determining the significant figures when all zeros are between two non-zero digits is that the zeros are considered significant.
• The significance of the trailing zeros in a number with a decimal point is that they are considered significant.
• The zeros in 4.700 m are considered significant because they are trailing zeros with a decimal point.
• The number 123000 mm has 4 significant figures.

Other Systems

• The MKS system is another system of units that uses meter, kilogram, and second as base units.
• The organization that developed the standard scheme of symbols, units, and abbreviations for the SI system in 1971 is the International Committee for Weights and Measures.
• Conversions within the SI system are considered simple and convenient because the units are based on the decimal system.

Angles

• The unit defined for plane angle dθ in SI is the radian (rad).
• The solid angle dΩ is defined in SI as the ratio of the area of the sphere subtended by the angle to the square of the radius of the sphere.

Learn about the SI units for plane angle (radian) and solid angle (steradian) which are both dimensionless quantities. Explore the definitions and symbols of radian (rad) and steradian (sr), along with other SI base quantities and units.