Maths: using units, standard form, decimal form

Measuring cell size

Cell size can be measured using an eyepiece graticule. The graticule has a scale ruled on it.

You must find out the distance measured for each division of the graticule. You can then use the graticule to measure cells. The distance will be different for each objective lens.

To do this, you will use a stage micrometer. You will use this to calibrate the eyepiece graticule. Once it is calibrated, you can use the eyepiece graticule every time you use the microscope.

Cell size can be measured using an eyepiece.

The distance of 250 μm on the stage micrometer lines up against two divisions at 10 and 61 on the eyepiece graticule.

61 - 10 = 51. Divisions on the eyepiece graticule are equivalent to 250 μm on the stage micrometer.

One division on the eyepiece graticule is equivalent to  \frac{250}{51} μm on the stage micrometer:

= 4.9 μm (to two significant figures).

Therefore one division is equal to 4.9 μm.

Using the same calibrated eyepiece graticule to measure a cell:

The calibrated eyepiece graticule can be used to make measurements of any cells or other structures viewed with the microscope on that magnification

The width of the cell highlighted = 52 - 40 = 12 eyepiece graticule divisions.

The real width of the cell is 12 × 4.9 μm = 59 μm (to two significant figures)

Question

What would be the length of a plant cell that was 35 divisions on this graticule? Give your answer to two significant figures.

170 μm.

Each eyepiece graticule division is 4.9 μm.

The real width of the cell is 35 × 4.9 μm = 171.5 μm.

To two significant figures, this is 170 μm.

Question

There are 1000 μm in 1 mm. The width of a cell measures 170 μm, what will the cell measure in mm?

170 ÷ 1000 = 0.17 mm.

The cell is 170 μm to convert it to mm divide by 1000.

The cell is 0.17 mm in width.

Calculating the magnification of an image

A student drew an image of the animal cell he saw under the microscope. The formula to calculate magnification is:

 \text{magnification} = \frac{size~of~image}{real~size~of~object}

The formula shown in a magnification triangle:

A triangle showing how to calculate the magnification of an image
Question

When measured, the width of the image drawn in the student's book was 40 mm. The actual size of the cell is 0.17 mm. Calculate the magnification of the image.

×235.

The size of the image drawn = 40 mm.

The real size of the cell is = 0.17 mm.

Magnification = 40 ÷ 0.17 = 235.