# Choose your units

Which units would you choose best to fit these situations?

## Problem

Some units are particularly well suited to a given measurement because they turn out to give a small, whole number of units. Understanding this concept gives you a feel for the order of magnitude of the quantities.

What units would you measure these quantities in to make an approximation which was a reasonably small whole number?

- The volume of a bacterium
- The mass of an oak tree
- The area of a leaf
- The half-life of Uranium-235
- The area of a football pitch
- The average lifespan of a human
- The volume of a bath tub

Can you reverse the process? For the following units, what physical phenomena might naturally be measured to be around 1 unit?

- Millimetre
- Newton
- Angstrom
- Joule
- Volt
- Microgram
- Micrometre
- Hertz
- Parsec

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## Student Solutions

### Phenomena to units

Volume of a bacterium - Cubic micrometres $\mathrm{\mu m}^3$Mass of an oak tree - Tonnes $(10^3\textrm{ kg})$

Area of a leaf - Square centimetres $(\textrm{cm}^2)$

Half-life of Uranium-235 - Millions of years

Area of a football pitch - Hectares

Average life-span of a human -Years

Volume of a bath tub - Cubic metres $(\textrm{m}^3)$

### Units to phenomena

Millimetre - size of an amoebaNewton - weight of an apple

Angstrom - atomic diameter of a hydrogen atom

Joule - kinetic energy of a table tennis ball travelling at $100\textrm{ km h}^{-1}$

Volt - voltage across an AA cell

Microgram - mass of $1\textrm{ mm}^3$ of air

Micrometre - mitochondrion

Hertz - frequency of tick-tock on a clock

Parsec - distance to Proxima Centauri (closest star other than the Sun)

## Teachers' Resources

### Why do this problem ?

Use of units is a critical skill in the sciences, and one which often leads to confusion. This problem will encourage students to understand the relationships between various types of units, as well as possibly introducing them to new important scientific units. It will also help to embed the important skill of checking numerical answers to see if they make sense in terms of orders of magnitude, along with a sense of where units are of relevance in science.### Possible approach

This question works well through discussion in pairs. Remind
the students that common sense works well when dealing with units:
for example, a cubic mm is clearly far smaller than the volume of a
bathtub.

### Key questions

What suggestions for units are possible in each case?

### Possible extension

Continue the question for other, more exotic units of measure (such as those given in New units for Old )### Possible support

Remind students the formulae for the compound measures, such
as volume.

Students might also struggle with the reasonably open nature
of the question. Remind them that there is no 'correct' answer and
common sense approximations will help.