The three common metric units are **metre** for length, **litre** for capacity and **gram** for mass.

Metric units are based on powers of 10, and the metric units (metre, gram, litre) are prefixed to indicate which power of 10 is being used:

**milli** means a thousandth (`frac(1)(1000)`)

**centi** means a hundredth (`frac(1)(100)`)

**kilo** means a thousand

Length | |

1 kilometre (km) | = 1000 metres (m) |

1 metre (m) | = 100 centimetres (cm) |

1 centimetre (mm) | = 10 millimetres (mm) |

Mass | |

1 tonne (t) | = 1000 kilograms (kg) |

1 kilogram (kg) | = 1000 grams (g) |

Capacity | |

1 litre (l) | = 1000 millilitres (ml) |

To convert between amounts, set up a small table for the conversion. On the first line, show the conversion rate. On the second line, put in the value to convert.

Dylan is putting up a shelf in an alcove. The alcove measures 1058mm. The shelf is 103cm long. Will the shelf fit?

Change the alcove from mm to cm. Create a small table showing that to get from cm to mm you multiply by 10. As you are starting off with mm, you must divide to get cm.

cm | --> | mm |

1 | x | 10 |

1058 ÷ 10 = 105.8 | 1058 |

The shelf is smaller than the alcove, so it will fit.

Answer: Yes

Mia is measuring out some liquid for a chemistry experiment. She needs 520cm^{3}. What is this in litres?

Change cubic centimetres to millilitres: 520cm^{3} = 520*ml*.

litre | --> | ml |

1 | x | 1000 |

520 ÷ 1000 = 0.520 | 520 |

Create a small table showing litres to millilitres. As you are going from millilitres to litres (the opposite way to the conversion) then it is a division.

Answer: 0.520 litres

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