Significant Figures and Scientific Calculations

Understanding Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. They are crucial in scientific calculations to reflect the precision of measured values.

• Definition: Significant figures indicate the precision of a measured or calculated quantity.

• 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: 75.052 g has 5 significant figures; 1.852 g has 4 significant figures.

Significant Figures in Calculations

When performing calculations, the number of significant figures in the result depends on the operation:

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

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

• Example: Subtracting 73.18 g from 75.052 g (both to the hundredths place) gives a result with 2 significant figures: g.

Unit Conversions

Converting Between Units

Unit conversions are essential in chemistry to express measurements in different units. This often involves multiplying by conversion factors that relate two units.

• Conversion Factor: A ratio that expresses how many of one unit are equal to another unit.

• Example: To convert 0.0921 nm to pm:

  • 1 nm = 1000 pm

Density and Unit Conversion

Density is a physical property defined as mass per unit volume. It can be converted between units using appropriate conversion factors.

• Formula:

• Example: To convert the density of gold from to :

  • Use the following conversion factors:

    • 1 lb = 453.592 g

    • 1 ft = 30.48 cm, so

  • (rounded to 3 significant figures)

Scientific Notation and Calculations

Using Scientific Notation

Scientific notation is used to express very large or very small numbers in a compact form. It is especially useful in chemistry for dealing with measurements at the atomic or molecular scale.

• Format: , where and is an integer.

• Example:

Calculations with Scientific Notation

• Multiplication: Multiply the coefficients and add the exponents.

• Division: Divide the coefficients and subtract the exponents.

Practice Problems and Applications

Sample Problems

1. Significant Figures in Subtraction: (2 significant figures)

2. Significant Figures in Division: (rounded to 2 significant figures)

3. Significant Figures in Addition: (rounded to 2 decimal places)

4. Significant Figures in Multiplication/Division: (rounded to 3 significant figures)

5. Scientific Notation Multiplication: (rounded to 4 significant figures)

Unit Conversion Examples

• Blood Glucose Concentration: Convert 122 mg/dL to g/L:

• Area Conversion: Convert to :

  • 1 in = 2.54 cm, so

Summary Table: Significant Figures Rules