Maths in biology

• Meter


  The base unit of measurement in science
• Sizes in biology


  • Often much smaller than a meter
• Centi


  One hundredth
• Centimeter (cm)


  One hundredth of a meter
• Size of objects


  • Width of little finger is around 1 cm
• Milli


  One thousandth
• Millimeter (mm)


  One thousandth of a meter
• Size of objects


  • Tip of a ballpoint pen is around 1 mm
• Micro


  One millionth
• Micrometer (μm)


  One millionth of a meter
• Size of objects


  • Typical human cell is around 10-20 μm in size
• Nano


  One billionth
• Nanometer (nm)


  One billionth of a meter
• Size of objects


  • Hemoglobin molecule is around 5 nm in diameter
• Prefixes centi, milli, micro, and nano are used to describe sizes in science
• Smaller units like micrometers and nanometers are used to describe the size of cells and their components
• Surface area to volume ratio

  Ratio of the surface area to the volume of an organism
• Single-celled organisms like amoeba have a huge surface area to volume ratio
• Single-celled organisms can rely on diffusion to transport molecules in and out of their cell
• Calculating surface area to volume ratio

  1. Calculate surface area

  2. Calculate volume

  3. Divide surface area by volume
• Organisms with different side lengths

  • 1 mm sides
  • 2 mm sides
  • 3 mm sides
• As organisms get larger


  The surface area to volume ratio falls sharply
• Multicellular organisms have a surface area that is not large enough for their volume
• How multicellular organisms solve the problem of low surface area to volume ratio

  • Have special structures for gas exchange with high surface area (e.g. lungs)
  • Have a transport system to carry gases around the body
• Gills


  Where gas exchange occurs in fish
• Adaptations of fish gills to increase rate of gas diffusion

  • Massive surface area from many fine filaments
  • Thin membrane for short diffusion pathway
  • Efficient blood supply to maintain concentration gradient