Quantity Expressed with Value and Unit

Q

How should a physical quantity be expressed?

✍: FYIcenter.com

A

When presenting a physical quantity, we need to present it with 2 components, the numerical value and the associated unit.

ISO 80000 specifies that the numerical value and the associated unit of a quantity should be expressed as a multiplication operation. For example:

<math> <mi>v</mi> <mo>=</mo> <mn>100</mn> <mo>⁢</mo>
  <mi mathvariant="normal">km</mi>
  <mo lspace="0" rspace="0">/</mo>
  <mi mathvariant="normal">h</mi> </math>
     v = 100 ⁢
      km
      /
      h 
where
    v is speed limit on highway
    100 is the numerical value 
    km/h is the unit
    "Invisible Times" operator is used 

Note that the above equation can be rearranged to express the numerical value of 100 as the speed limit v in km/h:

<math> <mn>100</mn> <mo>=</mo> <mi>v</mi>
  <mo lspace="thickmathspace" rspace="thickmathspace">/</mo>
  <mo>(</mo> <mi mathvariant="normal">km</mi>
  <mo lspace="0" rspace="0">/</mo>
  <mi mathvariant="normal">h</mi> <mo>)</mo> </math>
     100 = v
      /
      ( km
      /
      h ) 

ISO 80000 also includes another expression for the numerical value of a quantity symbol in a given unit with curly brackets:

<math> <msub><mrow> <mo>{</mo> <mi>v</mi> <mo>}</mo>
  </mrow> <mrow> <mi mathvariant="normal">km</mi>
  <mo lspace="0" rspace="0">/</mo>
  <mi mathvariant="normal">h</mi>
  </mrow> </msub> <mo>=</mo> <mi>v</mi> 
  <mo lspace="thickmathspace" rspace="thickmathspace">/</mo>
  <mo>(</mo> <mi mathvariant="normal">km</mi>
  <mo lspace="0" rspace="0">/</mo>
  <mi mathvariant="normal">h</mi> <mo>)</mo> </math>
      { v }
        km
      /
      h
        = v 
      /
      ( km
      /
      h ) 

 

⇒ Quantity Equation in Coherent Units

⇐ Quantities (Types) Included in ISQ

⇑ ISO/IEC 80000 - Quantities and units

⇑⇑ MathML (Mathematical Markup Language)

2026-10-28, ∼1928🔥, 0💬