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### Number and algebra

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# Bigger or Smaller?

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Age 14 to 16

Challenge Level

When measuring some property of an object the number we measure depends on the units chosen. For example, 1cm = 0.01m, so converting from cm to m makes the number get smaller; we need more small units to make up the number of big units. In each case below, does the number get bigger or smaller following a change in units? Can you estimate without a calculator an approximate factor by which the
numbers would change in each case?

- 1 cm $^2\rightarrow ??$ m $^2$
- 1 foot $\rightarrow ??$ inches
- 1 mile $\rightarrow ??$ kilometers
- 1 litre $\rightarrow ??$ cm $^3$
- 1 foot $^3\rightarrow ??$ inches $^3$
- 1 m s $^{-1}\rightarrow ??$ miles / hour
- 1 mm $^3\rightarrow ??$ m $^3$
- 1 degrees C $\rightarrow ??$ degrees K
- 85 degrees $\rightarrow ??$ radians
- 1 Pa $\rightarrow ??$ cm$^{-1}$ g s$^{-2}$
- 1 W $\rightarrow ??$ cm$^2$ g s$^{-3}$
- 1 Hz $\rightarrow ??$ per minute
- 1 Mol $\rightarrow ??$ trillion
- Molarity of 1$\rightarrow ??$ per cm$^3$
- 1 katal $\rightarrow ??$ million million per picosecond

Can you make up some of your own similar problems?

**Other problems**

Try the fun Zin Obelisk task from the main NRICH site