Using and Expressing Measurements
Measurements in science always include both a number and a unit. Scientific notation makes large or small numbers manageable by expressing them as a coefficient (between 1 and 10) multiplied by a power of 10 (like 6.02 × 10²³). When the exponent is positive, you're multiplying by 10; when negative, you're dividing by 10.
Working with scientific notation follows simple rules. For multiplication, multiply the coefficients and add the exponents (3×10⁴ × 2×10² = 6×10⁶). For division, divide the coefficients and subtract the exponents. When adding or subtracting, numbers must have the same exponent first.
Significant figures sig−figs show the precision of your measurement. All non-zero digits count as significant, along with zeros between other digits. Zeros before the first non-zero digit don't count, but those after a decimal point do. The number of sig-figs in your answer should match the measurement with the least precision.
💡 In calculations, your answer can never be more precise than your least precise measurement! For addition/subtraction, match decimal places; for multiplication/division, match sig-figs.
Accuracy refers to how close a measurement is to the true value, while precision shows how consistent repeated measurements are. Error can be calculated as:
- Error = experimental value - accepted value
- Percent error = |error|/accepted value × 100%
The International System of Units (SI) provides standard measurement units. Base units include meters (length), kilograms (mass), seconds (time), kelvin (temperature), and moles (amount). Prefixes like kilo- (×1000), milli- (÷1000), and micro- (÷1,000,000) let you scale units easily.
Temperature conversions are essential: K = °C + 273, and 20°C equals 68°F (room temperature). When converting between units, the actual quantity remains the same—just expressed differently, like how $1 equals 100 pennies.