# Measuring paper

##### Class practical

Measuring many sheets to find the thickness of one.

#### Apparatus and materials

*For each student group*

Pack of paper containing a known number of sheets (e.g. 500)

Sheet of the same paper

Ruler with millimetre scale (e.g. a metre rule)

Chemical balance

Micrometer (OPTIONAL)

Selection of rulers/tape measures with different scale divisions (OPTIONAL)

#### Health & Safety

#### Procedure

**a** Attempt to measure the thickness of a single sheet of paper. Fold the paper in half, in half again, and so on, to obtain multiple thicknesses. Measure the thickness and calculate the thickness of a single sheet.

**b** Measure the thickness of a pile of a known number of sheets (say, 100 or 200). Calculate the thickness of a single sheet.

**c** Compare these two methods for measuring the thickness of a single sheet. Which is better?

#### Teaching notes

**1** A book could be used instead of a pile of sheets of paper. Students should make a rough measurement of a pile of paper or the thickness of the book (remember the book is numbered on both sides of the paper).

**2** As well as the length, width and thickness of the paper, some students may attempt to measure its density. Often paper is sold with a g/m^{2} value on the packet (which is **not** a density) and so this may provide a value against which they could check their measured value.

Alternatively, a textbook can be used, but beware of the factor 1/2 since a book has half as many leaves as pages.

**3** To encourage order of magnitude estimates, you could go on to give pupils a rough value for the diameter of an atom so that they can calculate how many atoms would sit next to each other in the thickness of a piece of paper. For paper made of cellulose (which contains carbon, hydrogen and oxygen) then the average atomic diameter is probably only about 1.5 x 10^{-9} cm. Students who do not delight in using large numbers should not be dragged through these calculations.

There are excellent books, videos and web sites on Powers of ten. Classroom displays of large and small distance measurements with pictures of the objects measured will create a good background to this work.

**4** You could follow this up with the activity 'Practice in using large and small numbers', which can be downloaded from here.

**5 How Science Works extensions:** Although the measurement methods here are relatively straightforward, this provides an opportunity for students to design and carry out their own experiment. Emphasise that they should measure as accurately as possible and clearly explain how their method improves the quality of data collected. Get them to try and estimate the uncertainties in their results and to identify which measurement they feel has the greatest uncertainty.

You could encourage students to write a full plan/method before they begin. If they are to do this, make relevant teaching points about the importance of clear and unambiguous instructions. Each group/student could write a procedure, which is then passed on to a different group/student to carry out, exactly as written. The second group/student can then evaluate the information that they have been given.

*This experiment was safety-checked in October 2007*