Scientific Notation and Significant Figures

Introduction to Scientific Notation

Scientific notation is a method used in chemistry to express very large or very small numbers in a compact form. This is especially useful for representing measurements such as Avogadro's number, atomic masses, or concentrations.

• Scientific Notation: A number is written as the product of a coefficient (between 1 and 10) and a power of ten.

• General Form: a × 10n, where a is the coefficient and n is an integer exponent.

• Example: 0.00045 can be written as 4.5 × 10-4.

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. The number of significant figures reflects the precision of a measurement.

• Rules for Counting Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros are significant only if there is a decimal point.

• Example: 0.00450 has three significant figures (4, 5, and the trailing 0).

Applying Scientific Notation in Chemistry Calculations

When performing calculations, it is important to express answers in scientific notation with the correct number of significant figures. This ensures clarity and accuracy in reporting results.

• Multiplication and Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

• Addition and Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

Example Problem

Question: Express the number 0.0000000010 in scientific notation with the correct number of significant figures.

• Step 1: Move the decimal point so that only one nonzero digit remains to the left of the decimal: 1.0

• Step 2: Count the number of places the decimal was moved: 9 places to the right.

• Step 3: Write the number as:

• Significant Figures: The original number (0.0000000010) has two significant figures (the 1 and the trailing 0), so the answer should also have two significant figures.

Table: Examples of Numbers in Scientific Notation

Summary

• Scientific notation simplifies the expression of very large or small numbers in chemistry.

• Always match the number of significant figures in your answer to the precision of the original data.

• Proper use of scientific notation and significant figures is essential for clear and accurate scientific communication.