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Choose Your Units

Which units would you choose best to fit these situations?

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?

Other problems

Try the fun Zin Obelisk task from the main NRICH site