Scientists often make measurements. These need to be stated with the units of the quantity being measured, and the accuracy of the measurements.

Sometimes a measurement, using the standard SI unit, will give a very large or very small number that is inconvenient to write out in full. For example, the distance from the Sun to Pluto varies from 4,400,000,000,000 m to 7,300,000,000,000 m.

Mathematicians have a system for writing large numbers in a shortened way called standard form.

This involves writing the value digits of the number as a number between 1 and 10, and then writing that number multiplied by a power of ten to expand it back to the full number represented.

For example, the distances from the Sun to Pluto range from:

4,400,000,000,000 m = 4.4 × 10^{12} m

to

7,300,000,000,000 m = 7.3 × 10^{12} m

Another system to reduce the problem of very long numerical measurements uses a standard set of abbreviations to cut down the numbers that need to be written. For example, 1,000 metres is a kilometre, so instead of '1,000 m' scientists write '1 km'.

Multiple Size | Power of ten (x10²) | Prefix | Prefix abbreviation |
---|---|---|---|

1,000,000,000,000 | 12 | tera- | T |

1,000,000,000 | 9 | giga- | G |

1,000,000 | 6 | mega- | M |

1,000 | 3 | kilo- | k |

0.01 | -2 | centi- | c |

0.001 | -3 | milli- | m |

0.000001 | -6 | micro- | μ |

0.000000001 | -9 | nano- | n |

Using prefixes, the distances from the Sun to Pluto range from:

4,400,000,000,000 m = 4.4 × 10^{12} m = 4.4 terametres = 4.4 Tm

to

7,300,000,000,000 m = 7.3 × 10^{12} m = 7.3 terametres = 7.3 Tm

- Question
Which is larger: 360 kV or 3.6 MV?

360 kV = 360,000 volts

3.6 MV = 3,600,000 volts

So 3.6 MV is larger.