Orders of magnitude

Orders of magnitude

• Used to make approximate comparisons between numbers or objects
• if one number is about 10 times bigger than another
  • It is one order of magnitude bigger
• Show orders of magnitude using powers of 10

working it out

Larger number / smaller number

• If answer is less than 10
  • same order of magnitude
• if answer is around 10
  • then it is 10^1  / one order of magnitude bigger
• If answer is around 100
  • Then it is 10^2  / two orders of magnitude bigger

Example 1

if the size of a prokaryotic cell is of the order 1.2 X 10^-6m and eukaryotic cells are from 1 X 10^-5m to 1 X 10^-4m, estimate how the size of a prokaryotic cell compares to the size of:

A) the smallest eukaryotic cell

B) the largest eukaryotic cell

(to the nearest magnitude) 

Solutions

A) divide size of smallest eukaryotic cell by size of prokaryotic cell:

(1 x 10^-5)  /  (1.2 x 10^-6) = approximately 10 (10^1)

Therefore prokaryotic cell is one order of magnitude smaller than the smallest eukaryotic cells

B) divide size of largest eukaryotic cell by size of prokaryotic cell:

(1 x 10^-4)  /  (1.2 x 10^-6) = approximately 100 (10^2)

Therefore prokaryotic cell is two orders of magnitude smaller than the largest eukaryotic cell