## Units and Standards

1.2 Units and Standards

### Learning Objectives

By the end of this section, you will be able to:

- Describe how SI base units are defined.
- Describe how derived units are created from base units.
- Express quantities given in SI units using metric prefixes.

We define a **physical quantity** either by specifying how it is measured or by stating how it is calculated from other measurements.

Measurements of physical quantities are expressed in terms of **units**, which are standardized values.

### SI Units: Base and Derived Units

In any system of units, the units for some physical quantities must be defined through a measurement process. These are called the **base quantities** for that system and their units are the system’s **base units**. All other physical quantities can then be expressed as algebraic combinations of the base quantities. Each of these physical quantities is then known as a **derived quantity** and each unit is called a **derived unit**.

ISQ Base Quantity | SI Base Unit |

Length | meter (m) |

Mass | kilogram (kg) |

Time | second (s) |

Electrical current | ampere (A) |

Thermodynamic temperature | kelvin (K) |

Amount of substance | mole (mol) |

Luminous intensity | candela (cd) |

Check out a comprehensive source of information on SI units at the National Institute of Standards and Technology (NIST) Reference on Constants, Units, and Uncertainty.

### Metric Prefixes

SI units are part of the **metric system**, which is convenient for scientific and engineering calculations because the units are categorized by factors of 10.

Prefix | Symbol | Meaning | Prefix | Symbol | Meaning |

yotta- | Y | 10^{24} | yocto- | y | 10^{–24} |

zetta- | Z | 10^{21} | zepto- | z | 10^{–21} |

exa- | E | 10^{18} | atto- | a | 10^{–18} |

peta- | P | 10^{15} | femto- | f | 10^{–15} |

tera- | T | 10^{12} | pico- | p | 10^{–12} |

giga- | G | 10^{9} | nano- | n | 10^{–9} |

mega- | M | 10^{6} | micro- | μ | 10^{–6} |

kilo- | k | 10^{3} | milli- | m | 10^{–3} |

hecto- | h | 10^{2} | centi- | c | 10^{–2} |

deka- | da | 10^{1} | deci- | d | 10^{–1} |

**Practice!**

Complete the relationship: 1 millimeter = _____ meter. |

(a) 0.001 |

(b) 1000 |

(c) 0.01 |

(d) 100 |

Complete the relationship: 200 centimeters = 2 _____. |

(a) meters |

(b) micrometers |

(c) kilometers |

(d) millimeters |

Rank the following in order of increasing size (smallest to largest). |

(a) 1 millimeter, 1 decimeter, 1 picometer, 1 nanometer |

(b) 1 nanometer, 1 decimeter, 1 picometer, 1 millimeter |

(c) 1 decimeter, 1 picometer, 1 nanometer, 1 millimeter |

(d) 1 picometer, 1 nanometer, 1 millimeter, 1 decimeter |