# Unit Conversions

## Unit Conversions Revision

**Unit Conversions**

In an exam question, you may be asked to give your answer in a different **unit **than you normally use. To do this, you need to know how to **convert units**.

**SI Units**

**SI units** are the standard units we use to** measure** quantities. The main SI units are shown in the table below.

Quantity |
Unit |
Symbol |

time | second | \text{s} |

length | metre | \text{m} |

mass | kilogram | \text{kg} |

electric current | amp | \text{A} |

temperature | kelvin | \text{K} |

amount of a substance | mole | \text{mol} |

luminous intensity | candela | \text{cd} |

All other units can be made by **combining SI units**. You can work out which SI units make up another unit using the **equation** for that quantity.

**Example:** Express 1 \text{ N} (newton) in SI units.

**[2 marks]**

The newton is the unit of force and the equation we use to calculate force is \bold{F=ma}

The unit of mass is the kilogram \text{(kg)}

The unit of acceleration is metres per square second \text{(m/s}^2\text{)}

Because mass and acceleration are multiplied together in the equation, you multiply these units together.

\text{ N}=\textcolor{00d865}{\text{kg}} \times \textcolor{10a6f3}{\text{m/s}^2}=\text{kgm/s}^2Therefore,

\bold{1} \textbf{ N} \bold{=1} \textbf{ kgm/s} \bold{^2}

**Unit Prefixes**

**Prefixes** are used to avoid writing large numbers or standard form. You should be aware of the following prefixes and their meanings:

Prefix |
Symbol |
Standard Form |
Number |

giga | G | \times 10^9 | \times 1\, 000 \, 000 \, 000 |

mega | M | \times 10^6 | \times 1 \, 000 \, 000 |

kilo | k | \times 10^3 | \times 1 \, 000 |

milli | m | \times 10^{-3} | \times 0.001 |

micro | \mu | \times 10^{-6} | \times 0.000\, 001 |

nano | n | \times 10^{-9} | \times 0.000 \, 000\, 001 |

For example:

- 1 \text{ GW}= 10^9 \text{ W} = 1 \, 000 \, 000 \, 000 \text{ W}
- 5 \, \mu \text{m} = 5 \times 10^{-6} \text{ m} = 0.000 \, 005 \text{ m}.
- 2.5 \text{ kg} = 2.5\times 10^3 \text{ g} = 2500 \text{ g}
- 500 \text{ nm} = 500 \times 10^{-9} \text{ m} = 5 \times 10^{-7} \text{ m} = 0.000 \, 000 \, 7 \text{ m}

You should also know the meaning of the following words:

Name |
Number |
Standard Form |
Number of Zeros |

Thousand | 1 \, 000 | 1 \times 10^3 | 3 |

Million | 1 \, 000 \, 000 | 1 \times 10^6 | 6 |

Billion | 1\, 000 \, 000 \, 000 | 1 \times 10^9 | 9 |

**Common Conversions**

There are some common conversions you should also know.

**Miles**\bold{\rightarrow}**Kilometres**

There are 1.61 \text{ km} in every mile. This means we can use the following equations to convert between kilometres and miles:

\text{km}= \text{miles}\times 1.61 \, \, \, \, \, \, \text{ miles}=\dfrac{\text{km}}{1.61}

- \text{km}= the
**number of kilometres** - \text{miles}= the
**number of miles**

**Degrees **__Celsius____\bold{\rightarrow}__**Kelvin**

Absolute zero, 0\text{ K} is equal to -273 \degree \text{C}. This means we can use the following equations to convert between degrees Celsius and kelvin.

\text{K}=\degree \text{C} + 273 \, \, \, \, \, \, \degree \text{C}=\text{K} - 273

- \text{K}= the
**temperature in kelvin**\text{(K)} - \degree \text{C}= the
**temperature in degrees Celsius**(\degree \text{C})

**Tonne**\bold{\rightarrow}**Kilogram**

1 tonne is equal to 1000 kilograms. You therefore use the following equations to convert between tonnes and kilograms:

\text{kg}=\text{tonnes} \times 1000 \, \, \, \, \, \, \text{tonnes}=\dfrac{\text{kg}}{1000}

- \text{kg}= the
**number of kilograms** - \text{tonnes}= the
**number of tonnes**

## Unit Conversions Example Questions

**Question 1: **Express a charge of 1 \text{ C} of charge in SI units.

Use the following question to help you:

\text{charge}=\text{current} \times \text{time}**[2 marks]**

Current units – Amps \text{(A)}

Time units – Seconds \text{(s)}

Charge units – \text{A}\times \text{s} = As

So \bold{1} \textbf{ C} = \bold{1} \textbf{ As}

**Question 2: **How many bytes are there in 2 megabytes?

**[1 mark]**

So in 2 megabytes there are:

\bold{2 \, 000 \, 000} or \bold{2 \times 10^6} or \bold{2} \textbf{ million} bytes

**Question 3: **Convert room temperature (21 \degree \text{C}) to kelvin.

**[2 marks]**