# Units in Equations

Here are some common Units:

Property | Name | Symbol |
---|---|---|

Length | meter | m |

Mass | kilogram | kg |

Time | second | s |

Force | Newton | N |

Energy | Joule | J |

Per second | Hertz | Hz |

And we put Metric Number Prefixes in front of the symbol to write larger or smaller values:

Name |
The
Number |
Prefix |
Symbol |

trillion | 1,000,000,000,000 | tera | T |

billion | 1,000,000,000 | giga | G |

million | 1,000,000 | mega | M |

thousand | 1,000 | kilo | k |

hundred | 100 | hecto | h |

ten | 10 | deka | da |

unit |
1 |
||

tenth | 0.1 | deci | d |

hundredth | 0.01 | centi | c |

thousandth | 0.001 | milli | m |

millionth | 0.000 001 | micro | µ |

billionth | 0.000 000 001 | nano | n |

trillionth | 0.000 000 000 001 | pico | p |

Examples:

**km**:**k**for kilo,**m**for meter becomes**kilometer**(a thousand meters)**mm**:**m**for milli,**m**for meter becomes**millimeter**(a thousandth of a meter)**MN**:**M**for mega,**N**for Newton becomes**meganewton**(a million Newtons)**g**:**g**for gram, one symbol only is just the unit, so that is**grams****µs**: µ for micro,**s**for second becomes**microsecond**(a millionth of a second)

Now ... how do we us them in equations?

First: it is common to just **use the symbol** (such as km for kilometers).

## Adding and Subtracting

Use the **same units** when we add or subtract!

### Example: Sam is designing a new table. The old table is 2 m long. The new table should be 200 mm longer:

2 m + 200 mm = **?**

The units need to be the same!

We can choose m (meters) or mm (millimeters).

Let's choose mm. 1 m is 1000 mm, so:

2000 mm + 200 mm = 2200 mm

**Or** we could choose m:

2 m + 0.2 m = 2.2 m

## Multiplying and Dividing

When multiplying put the units next to each other

When dividing put the unit after "**/**"

Like this:

### Example: Alex walks 100 m in 80 seconds, what average speed is that?

Speed is distance/time

Speed = \frac{100 m}{80 s}= 1.25 m/s

100 divided by 80 is 1.25, and m divided by s is m/s

### Example: Hunter kicks a soccer ball. It goes from 0 to 32 m/s in 0.1 seconds. What is the acceleration?

Acceleration is:

\frac{Change in Velocity (m/s)}{Time (s)}

Put in the values we know:

Acceleration = \frac{32 m/s − 0 m/s}{0.1s}= 320 m/s^{2}

The "m/s" becomes "m/s /s" which is m/s^{2}

Sometimes there is a special unit that is made up of other units:

### Example: The soccer ball weighs 0.4 kg, what is the force of Hunter's kick?

We can use Newton's Second Law of Motion:

**F** = m**a**

The mass m = 0.4kg,

and we already calculated the acceleration: a = 320 m/s^{2}

F = 0.4 kg × 320 m/s^{2}

F = 128 kg m/s^{2}

1 Newton (N) is the usual measure of force, and equals 1 kg m/s^{2}, so:

F = 128 N