Chemistry and Measurements: Scientific Notation, Units, Significant Figures, and Matter Classification

Chemistry and Measurements

Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a compact form. It consists of a coefficient and a power of 10.

• Coefficient: A number between 1 and 10

• Power of 10: Indicates how many times the coefficient is multiplied or divided by 10

Examples:

• 100,000 = $1.0 \times 10^5$

• 0.000008 = $8.0 \times 10^{-6}$

Scientific notation is especially useful for handling measurements in chemistry, such as Avogadro's number or atomic masses.

Percentages

To determine a percentage, divide the part by the total (whole) and multiply by 100.

• Formula: $\text{Part/Total} \times 100$

SI and Metric Units

Chemistry uses the International System of Units (SI) and the metric system for measurements. The following table compares common units:

Measurement	Metric	SI
Volume	Liter (L)	Cubic meter (m3)
Length	Meter (m)	Meter (m)
Mass	Kilogram (kg)	Pounds (lb)
Temperature	Celsius (°C)	Kelvin (K)
Time	Second (s)	Second (s)

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one estimated digit. The rules for determining the number of significant figures are as follows:

Rule	Measured Number	Number of Significant Figures
All nonzero digits	5.006 kg	4
Zero at the end of a decimal number	50.1 L	3
Zero as a coefficient of a number written in scientific notation	5.74 × 103 g	3
Zero at the beginning of a decimal number	0.004 L	1
Zero at the end of a number with no decimal point	800 m	1

Density

Density is the mass of a substance divided by its volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

Example: If a 0.256 g sample of cholesterol is measured in a volume of 0.215 mL, the density is:

• $\text{Density} = \frac{0.256\ g}{0.215\ mL} = 1.19\ g/mL$

Conversion Factors

Conversion factors are used to change one unit to another. The process involves:

1. Identifying the given and needed units

2. Writing the conversion factor that cancels units and provides the needed unit

3. Setting up the calculation

Example: $1\ kg = 1000\ g$

Temperature Scales

The Kelvin temperature scale is based on absolute zero, the lowest possible temperature.

• Conversion: $K = ^\circ C + 273$

• To convert 45°C to K: $45 + 273 = 318\ K$

Matter and Its Classification

Pure Substances and Mixtures

Matter can be classified as pure substances or mixtures.

• Pure Substances: Elements and compounds with a fixed composition.

• Mixtures: Physical combinations of two or more substances.

Mixtures can be:

• Homogeneous: Uniform composition throughout (e.g., salt water).

• Heterogeneous: Non-uniform composition (e.g., salad).

Prefixes for SI Units

Prefixes are used to indicate multiples or fractions of units. The following tables summarize common prefixes:

Prefix	Symbol	Numerical Value	Scientific Notation	Equality
Giga	G	1,000,000,000	109	1 G = 1 × 109 units
Mega	M	1,000,000	106	1 M = 1 × 106 units
Kilo	k	1,000	103	1 k = 1 × 103 units
Deci	d	0.1	10-1	1 d = 1 × 10-1 units
Centi	c	0.01	10-2	1 c = 1 × 10-2 units
Milli	m	0.001	10-3	1 m = 1 × 10-3 units
Micro	μ	0.000001	10-6	1 μ = 1 × 10-6 units
Nano	n	0.000000001	10-9	1 n = 1 × 10-9 units

Specific Heat

Specific heat is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

• Formula: $q = SH \times m \times \Delta T$

• Where $q$ is heat (calories or joules), $SH$ is specific heat, $m$ is mass (g), and $\Delta T$ is temperature change (°C).

Example: To calculate the heat required to raise the temperature of 100 g of water by 10°C, with $SH = 1.00 \text{ cal/g}^\circ C$:

• $q = 1.00 \times 100 \times 10 = 1000 \text{ cal}$

Elements and Atoms

Students should know the abbreviations for elements, especially for atomic numbers 1–20, and selected others (e.g., 34, 35, 36, 53, 54).

Additional info: Some explanations and examples were expanded for clarity and completeness.