# 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).

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 = 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:

Change in Velocity (m/s) Time (s)

Put in the values we know:

Acceleration = 32 m/s − 0 m/s 0.1s = 320 m/s2

The "m/s" becomes "m/s /s" which is m/s2

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 = ma

The mass m = 0.4kg,
and we already calculated the acceleration: a = 320 m/s2

F = 0.4 kg × 320 m/s2

F = 128 kg m/s2

1 Newton (N) is the usual measure of force, and equals 1 kg m/s2, so:

F = 128 N