Scientific Notation and Significant Figure

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Scientific notation (Standard form)

  1. Scientific notation (also known as Standard index notation) is a convenient way to write very small or large numbers.
  2. In this notation, numbers are separated into two parts, a real number with an absolute value between 1 and 10 and an order of magnitude value written as a power of 10.

Significant Figure

  1. In measurement, significant figures relate the certainty of the measurement.
  2. As the number of significant figures increases, the certainty of the measurement increase, which means we are more certain about what we have measured.

Example:
Speed of light in a vacuum
= 299 792 458 ms-1
= 3.00 x 108 ms-1 (to 3 significant figures)

Example:
Write the number of significance figure (s.f.) of the following value:

  1. 135 m, (____s.f.)
  2. 0.013s (____s.f.)
  3. 0.2000A (____s.f.)
  4. 25.10 g (____s.f.)
  5. 3700km (____s.f.)
  6. 0.003kg (____s.f.)
  7. 1.54  10-3 (____s.f.)
  8. 0.001200 (____s.f.)

Answer:

  1. 135 m, ( 3 s.f.)
  2. 0.013s ( 2 s.f.)
  3. 0.2000A ( 4 s.f.)
  4. 25.10 g ( 4 s.f.)
  5. 3700km ( 4 s.f.)
  6. 0.003kg ( 1 s.f.)
  7. 1.54 x 10-3 ( 3 s.f.)
  8. 0.001200 ( 4 s.f.)