Units, Measurement, and Scientific Notation

Learning Objectives

Identify the seven base units of the SI system.

Use metric prefixes to convert between units.

Express very large and very small numbers using scientific notation.

Explain the importance of significant figures in measurements.

The Language of Measurement: The SI System

The International System of Units (SI) is the modern form of the metric system and the most widely used system of measurement. It is built upon seven base units.

The Seven SI Base Units:

1.Meter (m): Length

2.Kilogram (kg): Mass

3.Second (s): Time

4.Ampere (A): Electric Current

5.Kelvin (K): Thermodynamic Temperature

6.Mole (mol): Amount of Substance

7.Candela (cd): Luminous Intensity

All other units (like joules, newtons, volts) are derived units, formed by combinations of these base units.

Metric Prefixes

The metric system uses prefixes to denote multiples or fractions of the base units.

Kilo- (k): 1,000 (10³)

Centi- (c): 0.01 (10⁻²)

Milli- (m): 0.001 (10⁻³)

Micro- (µ): 0.000001 (10⁻⁶)

Nano- (n): 0.000000001 (10⁻⁹)

Example: 1 kilometer (km) = 1,000 meters. 1 milligram (mg) = 0.001 grams.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is written in the form:

a x 10ᵇ

where a is a number between 1 and 10, and b is an integer.

Examples:

The speed of light, 300,000,000 m/s, is written as 3.0 x 10⁸ m/s.

The diameter of a red blood cell, 0.000007 m, is written as 7 x 10⁻⁶ m.

Significant Figures

Significant figures are the digits in a number that are reliable and necessary to indicate the precision of a measurement.

When multiplying or dividing measurements, the result should have the same number of significant figures as the measurement with the fewest significant figures.

When adding or subtracting, the result should be rounded to the same number of decimal places as the measurement with the fewest decimal places.

This prevents a calculated result from appearing more precise than the measurements used to derive it.

Key Terms

SI Units: The International System of Units, the modern form of the metric system and the most widely used system of measurement. It is based on seven base units.
Scientific Notation: A method of expressing numbers as a product of a number between 1 and 10 and a power of 10.
Significant Figures: The digits of a number that are used to express it to the required degree of accuracy, starting from the first non-zero digit.
Kilogram (kg): The SI base unit of mass.