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A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

### More or Less?

Are these estimates of physical quantities accurate?

# Big and Small Numbers in Physics

### Why do this problem?

The ability to work with big and small numbers is a very important scientific skill. These questions provide a variety of contexts where handling such numbers is necessary, while offering practice at identifying key information and making decisions about estimates and assumptions.

### Possible approach

These questions could be used individually as starters or fillers within lessons. Alternatively, a class could work on different questions in small groups and then present their answers with reasoning to the rest of the class to stimulate discussion. Some questions can be tackled with little specialist knowledge; others may require research and additional information, as well as some assumptions, in order to come up with an answer.
It is important to stress that there is no "correct" answer for some of these questions - the value of this task comes from having a go at estimating and calculating with big and small numbers, and discussing assumptions that need to be made and extra data that need to be sought in order to find a solution.