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## Physical quantity

A physical quantity is something you can measure.

Examples:

• Length, $$l$$
• Weight (mass), $$m$$
• Speed, $$v$$
• Voltage, $$U$$
• Cost

## Unit

A unit is a definite magnitude of a certain physical quantity.

Examples:

• Length, $$l$$ – meter/metre, $$\text{m}$$
• Weight (mass), $$m$$ – gram, $$\text{g}$$
• Speed, $$v$$ – meters per second, $$\text{m/s}$$
• Voltage, $$U$$ – volt, $$\text{V}$$
• Cost – € (Euro) etc.

### SI units

Get used to them!

• Mass: 1 kg = 1000 g
• Volume: 1 L = 1 dm3 = 1000 mL

Also: Learn the prefixes:

 Prefix Base 10 Name Symbol mega M 106 kilo k 103 deci d 10–1 milli m 10–3 micro μ 10–6

## Numerical magnitude

The amount (magnitude) of the unit you’re measuring.

Examples:

 Phys. quant. Example Numerical magnitude Length $$l = 1.93\text{m}$$ 1.93 Mass $$m = 250\text{g}$$ 250 Speed $$v = 25\text{m/s}$$ 25 Voltage $$U = 12\text{V}$$ 12

## The relation between physical quantity, magnitude, and unit Note: There is a multiplication sign between "$$250$$" and "$$\text{g}$$": $$m = 250 \times \text{g}$$

• This is similar to algebraic notation, e.g. $$y = 250x$$.

## How to use physical quantity, magnitude, and unit

### Example 1

If I dissolve 25g salt in 0.5dm3 water, which is the salt concentration? Give your answer in the unit g/dm3.

#### Solution

Since the answer is to be given in the unit $$\frac {\text{g}}{\text{dm}^3}$$, I have to divide the mass $$m$$ by the volume $$V$$. We write the concentration $$c$$:

$c = \frac {m}{V} = \frac {250\text{g}}{0.5\text{dm}^3} = 50 \frac {\text{g}}{\text{dm}^3}$

Answer: $$c = 50\text{g/dm}^3$$

↑ Note: Both physical quantity, magnitude, and unit in the answer!

### Example 2

A salt solution has a concentration of 50g/dm3. From this solution I pour 0.100dm3 in a glass. What is the mass of the salt in the glass?

#### Solution

I want to know the mass $$m$$, which is measured in $$\text{g}$$.

I know the concentration $$c$$, which is measured in $$\frac {\text{g}}{\text{dm}^3}$$.

How do we go from the unit $$\frac {\text{g}}{\text{dm}^3}$$ to $$\text{g}$$? We must multiply $$\frac {\text{g}}{\text{dm}^3}$$ with $$\text{dm}^3$$:

$\frac {\text{g}}{\text{dm}^3} \times \text{dm}^3 = \text{g}$

Thus, we can write:

$m = cV = 500\frac {\text{g}}{\text{dm}^3} \times 0.100\text{dm}^3 = 50.0\text{g}$

Answer: $$m = 50.0\text{g}$$

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