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Simple Explanation:
Introduction to Scientific Notation
Scientific notation is the standard method of simplifying large or small numbers into a compact format by multiplying or dividing by powers of ten. In scientific notation, the number must start with a digit in the ones place, followed by decimals, and then multiplied by the appropriate power of ten.
For example:
A large number like 3,600,000 can be written as 3.6×10⁶ in scientific notation.
A small number like 0.00045 can be written as 4.5×10⁻⁴ in scientific notation.
Quick tips:
Large Numbers: Count the number of digits behind the first digit. Simplify and use this count as the exponent for 10.
Small Numbers: Count the number of digits ahead of the first non-zero digit. Simplify and use this count as the negative exponent for 10.
Rules of Significant Figures
Non-zero numbers, zeros between non-zero numbers (e.g. 506), and all zeros to the right of a decimal (e.g. 0.0500) are significant figures.
Placeholder zeros (e.g. 0.0123 and 6900) aren’t significant figures, and to remove them, use scientific notation.
Sig Figs in Addition or Subtraction - The result should have the same number of decimal places as the measurement with the fewest decimal places.
E.g. 123.4 mL - 69.25 mL = 54.2 mL (Original answer is 54.15.)
Sig Figs in Multiplication or Division - The result should have the same number of significant figures as the measurement with the fewest significant figures.
E.g. 125 cm × 69 cm × 506.00 cm = 4400000 cm (Original answer is 4364250.)
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