# Cell size

Most animal and plant cells are 0.01 – 0.10 mm in size. The smallest thing seen with the naked eye is about 0.05 mm.

For all cells we need a microscope to see them in any detail.

The best unit to measure most cells is the micrometre, symbol μm.

For some structures, for instance , or organisms such as , it’s best to use a smaller unit – the nanometre, symbol nm.

One metre can be broken down into the following measurements:

Millimetre, mmMicrometre, μmNanometre, nm
$\frac{1}{1000}\; metre$$\frac{1}{1000}\; millimetre$$\frac{1}{1000}\; micrometre$
Division of a metre as a fraction$\frac{1}{1000}\; metre$$\frac{1}{1\: 000\: 000}\; metre$$\frac{1}{1\: 000\: 000\: 000}\; metre$
Division of a metre in standard form1 × 10-3 m1 × 10-6 m1 × 10-9 m

### Standard form

When writing and working with very large or very small numbers, we use .

Standard form shows the size of numbers as powers of ten.

Standard form numbers are written as:
• A × 10n
• A is a number greater than one but less than 10
• n is the index or power, always in powers of 10

### Using standard form for large numbers

• A population of 120 000 000 microorganisms could be written as 1.2 × 108.
• This number can be written as 120 000 000.0.
• If the decimal place is moved eight spaces to the left we get 1.2.
• So we put x 108 after 1.2 to show this.
• Because the original number is greater than one metre the minus sign before the 8 is not needed.
• It makes a very large number easier to write down.

### Using standard form for small numbers

• A red blood cell's diameter of 7 μm or 0.000007 m could be written as 7 × 10-6 m.
• This number can be written as 0.000007.
• If we move the decimal place six spaces to the right we get 7.0
• So we put x 10-6 after 7 to show this.
• Because the original number is less than one metre we put a minus sign before the 6.
• It makes a very small number easier to write down.

## Calculating the magnification of a cell

In a book, a of the cell measured 100 mm.

The real size of the cell shown is 0.05 mm.

To calculate the magnification:

$magnification = \frac{100\; mm}{0.05\; mm} = 2000$

It’s important to work in the same units when calculating magnification. Sizes of most cells are given in micrometres, symbol μm.

To calculate magnification using the same formula in micrometres, convert the measurement of the cell above from mm into micrometres:

Cell measurement = 100 mm

1 mm = 1000 μm

100 mm = 100 x 1000 μm

100 mm = 100 000 μm

The real size of the cell above in micrometres is 50 μm.

The magnification of the image:

$magnification = \frac{100\; 000 \; μm}{50\; μm} = 2000$

From this we know that the image has been magnified 2000 times.