Significant Figures

The significant figures in a measurement include all the digits that can be known precisely plus a last digit that must be estimated

Rules:

• Every non-zero digit in a recorded measurement is significant
• Zero Rules:
  • Leading Zeros- zeros that precede all the non-zero digits; NEVER count as sig-figs
    • eg. 0.00832-- 3 sig-figs
    • eg. 0.23-- 2 sig-figs
  • Captive Zeros- zeros between non-zero digits; are counted as sig-figs
    • eg. 7003-- 4 sig-figs
    • eg. 409.076-- 6 sig-figs
  • Trailing Zeros- zeros at the right end of a number; only count as sig-figs when there is a decimal point
    • eg. 456200-- 4 sig-figs
    • eg. 50938.00-- 7 sig-figs
• Exact Numbers
  • Obtained by counting, not by measuring devices
  • Can be assumed to have an unlimited amount of sig-figs
  • Can come from definitions
    • eg. 1 in.=2.54 cm
• Multiplying and Dividing sig-figs
  • The answer must contain no more sig-figs than the measurement with the least sig=figs
  • The position of the decimal point is irrelevant
    • eg. 5.89 x 4.5 = 27
• Adding and Subtracting sig-figs
  • The answer must contain the same number of sig-figs to the right of the decimal point as the measurement with the fewest sig-figs to the right of the decimal point
    • eg. 61.2 = 9.621 = 70.2

Scientific Notation

Chemists use scientific notation is used for very large or small numbers

• eg. the mass of a hydrogen atom is 0.00000000000000000000000167 grams
• eg. 2.0 grams of hydrogen is composed of 602000000000000000000000 hydrogen molecules

Numbers are written as the product of two numbers:

• A coefficient
• A power of 10 with an exponent
  • The exponent tells you how many times you multiply a number by 10
  • Numbers greater than 1 have a positive exponent (# of places the decimal moves left)
  • Numbers less than 1 have a negative exponent (# of places the decimal moves right)
    • eg. The number 23000 is written in exponential form as 2.3 x 10^4
    • eg. 0.000051 is written in exponential form as 5.1 x 10^-5
  • Numbers between 1 and 10 do not need scientific notation
    •  eg. 9 = 9 x 10⁰
    • 1.2 = 1.2 x 10⁰
    • 7.562580 = 7.562580 x 10⁰
      • All have an exponent of zero (10⁰ = 1)