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# Units and Prefixes

## Units and Prefixes

In Physics we are often concerned with measuring. There is an international system of units that is used by scientists worldwide. This is known as the SI system, ( Systmem Internationale).

The base units in this system are:

**Mass:- **measured in Kilograms (**kg**)

**Length:-** measured in metres (**m**)

**Time:-** measured in seconds (**s**)

**Current:-** measured in amperes (**amps.A**)

**Temperature:-** measured in Kelvin (**K**)

Other quantities are also measured in particular units derived from the above.

Examples of these derived units are:

**Speed:-** measured in metres per second (**m/s**)

**Force:-** measured in newtons (**N**)

**Energy:-** measured in joules ( **j** )

**Charge:-** measured in coulombs (**C**)

**Voltage:-** measured in volts (**V**)

There are more units which I will introduce within other hubs as I go along.

Sometimes the size of the quantity being measured is much too large or small for the appropiate unit. In this situation we use multiples of the unit denoted by standard prefixes.

**The common prefixes used at GCSE are:**

**Prefix **nano micro milli kilo mega giga

**Factor **10^{-9 }10^{-6 }10^{-3 }I 10^{3 }10^{6 }10^{9}

**Symbol **n μ m k **M G**

In these cases the unit is multiplied by the factor,

for example:

**5 milliamps (5mA) = 5 x 10 ^{-3 }A**

**Now try the following:-**

**1. Convert 20km to m**

**2. How many amps is 30 μA?**

**3. What is 5000m in km?**

**4. Give 40000joules in MJ**

## Workings of examples

**1. Convert 20km to m**

**On the calculator:**

Multiply

** 20 x the factor of the symbol km**

**= 20 x 10 ^{3}**

**= 20000m**

If the case is that your calculator isn't handy it can be done by this alternative method:

**20 = 2 x 10 ^{1}**

^{}** = 2 x 10 ^{1 }x 10^{3} (remember when multiplying you add the indices)**

** = 2 x 10 ^{4} (10^{4} means you have four zeros, therefore the answer is 20000)**

** = 20000m**

**2. How many amps is 30 μA ?**

**On the calculator:**

Multiply

30 x the factor of the symbol **μ**

**= 30 x 10 ^{-6}**

^{}= 3 x 10^{-5}

^{}

To do it manually without the calculator:

**30 = 3 x 10 ^{1}**

^{}** = 3 x 10 ^{1} x 10^{-6 }(remember when multiplying you add the indices)**

** = 1 + (-6) = -5 (therefore)**

** = 3 x 10 ^{-5}A**

^{}

^{}

**3. What is 5000m in km?**

**Remember there is 1000m in a km.**

Quite simply you could divide by 1000 and get the answer as 5km.

**On the Calculator:**

Multiply

5000 x the factor by the symbol **m**

**= 5000 x 10 ^{-3}**

**= 5km**

To do it manually without the calculator:

**5000 = 5 x 10 ^{3}**

** = 5 x 10 ^{3} x 10^{-3}**

** = 3 - 3 = 0 (therefore)**

** = 5km**

**4. Give 40000joules in MJ**

**1 megajoule = 1 000 000 joules**

**On the Calculator:**

Multiply

40000 x the factor of the symbol **j**

**In this case we don't have it in the above table, so we are going to divide by the factor MJ, which means our answer will be a fractional one, so it will have a negative ^{power.}**

**Divide**

40000 x the factor of the symbol **M**

** =** **40000 ÷ 10^{6}**

^{} ** = 4 x 10 ^{4 }÷ 10^{6 }**

** = 0.04 MJ or 4 x 10 ^{-2 }MJ**

To do it manually without the calculator:

**40000 = 4 x 10 ^{4}**

^{} = 4 x 10^{4} ÷ 10^{6} ( when dividing remember to subtract the indices)

**= 4 - 6 = -2**

** = 4 x 10 ^{-2 }MJ**

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