Unit 0: Fundamentals – Introduction to the Metric System and Scientific Notation

Metric System: Overview and Base Units

The metric system is a decimal-based system of measurement used worldwide in science, including biology. It is based on powers of ten, making conversions straightforward. The three primary base units are:

• Meter (m): The base unit for length.

• Gram (g): The base unit for mass.

• Liter (L): The base unit for volume.

Prefixes are added to these base units to indicate multiples or fractions of ten.

Metric Prefixes and Their Values

Metric prefixes represent different powers of ten and are used to express measurements at various scales. The following table summarizes common metric prefixes:

Mnemonic: "Kids Hop Down Mountain Drinking Chocolate Milk Making" can help remember the order of prefixes from kilo to micro.

Conversions within the Metric System

Converting between metric units involves moving the decimal point according to the difference in powers of ten between the units. The process is as follows:

• From larger to smaller units: Move the decimal point to the right (multiply).

• From smaller to larger units: Move the decimal point to the left (divide).

• Always add a decimal to the end of whole numbers before converting (e.g., 35 becomes 35.0).

• Count the number of steps between units to determine how many places to move the decimal.

Example: To convert 360 centimeters (cm) to decameters (dam):

• There are 3 steps from cm to dam (cm → m → dam).

• Each step is a power of ten, so divide by .

Frequently Used Metric Units in Biology

Biology commonly uses the following metric units:

• Milliliters (mL) and Microliters (μL): For measuring small volumes.

• Grams (g) and Milligrams (mg): For measuring mass.

• Meters (m), Centimeters (cm), Millimeters (mm), Nanometers (nm): For measuring length and microscopic structures.

Temperature Conversion: Celsius and Fahrenheit

Temperature in biology is usually measured in degrees Celsius (°C), which is based on the freezing and boiling points of water. The Celsius scale is also called the centigrade scale because there are 100 degrees between freezing (0°C) and boiling (100°C).

• Conversion formula:

Alternatively, as shown in the notes:

Example: Human body temperature is approximately 98.6°F, which converts to 37°C.

Conversions Between Metric and English Systems

In some cases, measurements must be converted between the metric system and the English (imperial) system. Common conversions include:

Scientific Notation

Scientific notation is a method for expressing very large or very small numbers in a compact, standardized form. It is especially useful in biology for measurements at the cellular or molecular level.

• Format: A number is written as a coefficient between 1 and 10 multiplied by a power of ten.

• Example: represents 342,000,033,994.

• Example: represents 0.0342000033994.

• To convert a number to scientific notation, place the decimal after the first non-zero digit and count how many places the decimal was moved. This number becomes the exponent.

Steps for Conversion:

1. Move the decimal point so that only one non-zero digit remains to its left.

2. Count the number of places the decimal moved; this is the exponent.

3. If the original number is greater than 1, the exponent is positive; if less than 1, the exponent is negative.

Example: 1234567 becomes ; 0.001234567 becomes .

Practice Problems

• Convert the following numbers from full expression to scientific notation:

• 456000000 →

• 0.00006785544 →

Additional info: The notes provide foundational skills for laboratory work and data analysis in biology, including measurement, conversions, and expressing values in scientific notation.