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Bigger or Smaller?

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. 1 cm $^2\rightarrow ??$ m $^2$
  2. 1 foot $\rightarrow ??$ inches
  3. 1 mile $\rightarrow ??$ kilometers
  4. 1 litre $\rightarrow ??$ cm $^3$
  5. 1 foot $^3\rightarrow ??$ inches $^3$
  6. 1 m s $^{-1}\rightarrow ??$ miles / hour
  7. 1 mm $^3\rightarrow ??$ m $^3$
  8. 1 degrees C $\rightarrow ??$ degrees K
  9. 85 degrees $\rightarrow ??$ radians
  10. 1 Pa $\rightarrow ??$ cm$^{-1}$ g s$^{-2}$
  11. 1 W $\rightarrow ??$ cm$^2$ g s$^{-3}$
  12. 1 Hz $\rightarrow ??$ per minute
  13. 1 Mol $\rightarrow ??$ trillion
  14. Molarity of 1$\rightarrow ??$ per cm$^3$
  15. 1 katal $\rightarrow ??$ million million per picosecond

Can you make up some of your own similar problems?

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