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Welcome to our Physics lesson on **What are multiples and submultiples of units?**, this is the second lesson of our suite of physics lessons covering the topic of **Units. Systems of Units. Fundamental and Derived SI Units**, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Multiples and submultiples are the prefixes that we frequently use to express or show quantities in scientific terminology. We use the Greek terms to write the multiples and submultiples in words and standard notation to express them in numbers. Some of the most important multiples and submultiples are shown in the table below:

Prefix | Meaning | Expression in numerical form | Expression in standard form |
---|---|---|---|

Peta (P) | One quadrillion | 1,000,000,000,000,000 | 1015 |

Tera (T) | One trillion | 1,000,000,000,000 | 1012 |

Giga (G) | One billion | 1,000,000,000 | 109 |

Mega (M) | One million | 1,000,000 | 106 |

Kilo (k) | One thousand | 1,000 | 103 |

Hecto (h) | One hundred | 100 | 102 |

Deca (da) | Ten | 10 | 101 |

Unit | One | 1 | 100 |

Deci (d) | One tenth | 0.1 | 10-1 |

Centi (c) | One hundredth | 0.01 | 10-2 |

Milli (m) | One thousandth | 0.001 | 10-3 |

Micro (μ) | One millionth | 0.000 001 | 10-6 |

Nano (n) | One billionth | 0.000 000 001 | 10-9 |

Pico (p) | One trillionth | 0.000 000 000 001 | 10-12 |

Femto (f) | One quadrillionth | 0.000 000 000 000 001 | 10-15 |

As you see, when approaching the unit, the divisions become finer (the highlighted part of the table). However, prefixes such as hecto, deca, deci and centi are not officially recognized in the SI system.

When we appoint a certain unit to a prefix, we obtain a multiple or submultiple of the unit itself. Thus, if we say 1 micrometer, we understand a length equal to one millionth of a meter. If we say one milligram, we understand a mass equal to one thousandth of a gram or one millionth of a kilogram (remember that kilogram, not gram, is the unit of mass) and so on.

The generic rule of SI units (with few exceptions) is that the units change by powers of ten. Only for the multiples of the unit of time (second) we use different rules. Thus, 1 min = 60s, 1 hr = 60 min, 1 day = 24 hr and so on. In this case, the base 12 numerical system is used for historical reasons. On the other hand, the submultiples of second obey to the "powers of ten" rule. We can say millisecond, microsecond, nanosecond etc.

As for the Imperial System of units, the conversion rules are different. Thus, for the units of length we have:

- 1 inch (2.54 cm) = 1/12 foot
- Therefore, 1 foot = 12 × 2.54 cm = 30.48 cm
- 1 yard = 3 feet = 3 × 12 inches = 36 inches = 91.44 cm
- 1 mile = 1760 yard = 1609 m

and so on. As for the units of mass in the Imperial System of Units, we have

- 1 lb = 16 oz (ounces) = 0.4536 kg
- Thus, 1 oz = 0.454 / 16 = 0.0283 kg = 28.3 g
- 1 oz = 16 drams and so on.

As for the multiples of pound, we have

- 1 ton = 2000 lbs = 2000 × 0.454 kg = 908 kg

A French tourist is shopping in London. He wants to buy some oranges. The price of the oranges is 0.80 ₤/lb. How many kg of oranges can he buy with ₤20?

First, let's calculate how many lbs of oranges the tourist can buy with ₤20. We have:

Amount in lbs = *Amount of money (in ₤)**/**Price (in ₤)* = *20**/**0.80* = 25 lbs

Now, let's convert lbs to kg using the known conversion factor. We have

Amount in kg = Amount in lbs × lb to kg conversion factor

= 25 lbs × 0.454*kg**/**lb*

= 11.35 kg

= 25 lbs × 0.454

= 11.35 kg

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- Continuing learning units and measurements - read our next physics tutorial: Length, Mass and Time

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