Metric System

Module 2.0: The Metric System

Introduction

• The United States is one of only three countries in the world that do not primarily use the metric system. The other two countries are:

  • Burma

  • Liberia

• Officially, the US uses the English (standard) measurement system.

• Despite this, the metric system is prevalent in everyday contexts such as food, vehicles, sports, etc.

Metric Base Units Measurement

• The basic metric units are as follows:

  • Length: Meters (m)

  • Volume: Liters (L)

  • Mass or weight: Grams (g)

  • Temperature: Degrees Celsius (°C)

  • Time: Seconds (s)

Prefixes for Base Units

• Base units may be inconvenient for certain measurements (e.g., measuring small lengths).

• Prefixes are added to the base units to create smaller or larger units based on powers of 10.

• Examples of the six most common prefixes:

• The addition of a prefix changes the unit by a multiple or fraction of 10.

Metric Units Overview

Metric Length in Biology

• The meter is the fundamental unit of length in the metric system.

• Biological life exists at various sizes, from large organisms like trees to microscopic entities like bacteria and viruses.

• Understanding metric prefixes is essential for comprehending the sizes of organisms or their components studied in biology.

• Size relationships of pertinent biological objects should be noted, along with their respective metric prefixes.

Common Metric Length Conversions

• Here are relevant relationships between the metric and English units of length:

  • 1 kilometer (km) = 0.62 miles (mi) or 5/8 mi

  • 1 meter (m) = 1.09 yards (yd) or 39.4 inches (in)

  • 1 centimeter (cm) = 1.2 inches (in)

  • 1 mile (mi) = 1.6 kilometers (km)

  • 1 yard (yd) = 0.91 meters (m)

  • 1 inch (in) = 2.54 centimeters (cm)

Metric Volume in Biology

• The typical adult human has approximately 5 liters (L) of blood.

• Medicinal dosages are commonly administered in milliliters (mL).

• The units of volume in the metric system are frequently used in scientific and medical contexts.

Thinking in Metric Units of Volume

• Key conversions related to volume:

  • 1 liter (L) ≈ 1.057 quarts

  • 1 milliliter (mL) = 1 cubic centimeter (cc)

  • 1 teaspoon ≈ 5 mL

  • 12 oz. soda ≈ 360 mL

  • 1 pint = 0.47 L

  • 1 cup = 240 mL

  • 1 fluid ounce = 30 mL

  • 1 gallon = 3.8 liters (L)

Metric Mass in Biology

• The average weight of an American adult female is around 74.7 kilograms (kg), equivalent to 164.7 pounds (lb).

• The average mass of an adult human brain is approximately 1300 grams (g).

• Mass is crucial when discussing sizes of organisms or parts of organisms, particularly in medicinal contexts where dosages are provided in milligrams (mg) or micrograms (µg).

Thinking in Metric Units of Mass

• Important mass conversions:

  • 1 kilogram (kg) = 2.2 pounds (lb)

  • 1 gram (g) is roughly equivalent to the weight of a paper clip

  • A 154 lb person weighs about 70 kg

  • 1 pound (lb) = 0.454 kg

  • 1 ounce (oz) = 28 grams (g)

Thinking in Metrics: Temperature

• Temperature in the metric system is expressed in degrees Celsius (°C):

  • 0° Celsius = freezing point (32° F)

  • 10° Celsius = cold (50° F)

  • 20° Celsius = cool (68° F)

  • 30° Celsius = warm (86° F)

  • 40° Celsius = hot (104° F)

Practice Problems

• Fill in the blanks:

  1. In Europe, gasoline is sold by the metric volume unit, which is the liter.

  2. Normal body temperature in the metric system is 37 degrees Celsius.

  3. The average height of a college student is about 1.60 meters tall.

  4. A kilogram (kg) weighs 1000 times more than a gram.

  5. A millisecond (ms) is 0.001 seconds.

How to Convert Within the Metric System

• Conversion methods include:

  • Number Line Method

  • Stair Step Method

  • Dimensional Analysis

• Mastery of these conversion strategies is critical for application in biology and relevant professional environments.

Number Line Method

• A number line used for metric conversions consists of 13 vertical lines, each representing a factor of 10.

Visual Representation of Metric Prefixes

• Example layout indicating prefixes from kilo to nano:

  • kilo ---- base ---- deci ---- centi ---- milli ---- micro ---- nano

Conversion Steps Using the Number Line

1. Identify the starting point on the number line.

2. Identify the endpoint on the number line.

3. Count the number of lines between each point.

4. Identify the direction of movement from “start” to “end.”

5. Move the decimal point of the original number that many spaces in the identified direction, filling in spaces with zeroes as needed.

Example Conversion

• Convert 53 milligrams (mg) to micrograms (µg):

  1. Starting point = milli

  2. Endpoint = micro

  3. Move 3 spaces to the right.

  4. Final answer: 53 milligrams = 53,000 micrograms.

Practice Example

• How many centigrams are in 5 grams?

  1. Identify starting (grams) and stopping (centigrams) points.

  2. Move 2 spaces to the right.

  3. Final calculation: 5 grams = 500 centigrams.

Stair Step Method

• This method visually represents the number line as stairs, with each step corresponding to a tenfold change in size.

Practical Stair Step Example

• How many millimeters are there in one decimeter?

  • Starting point = decimeter; stopping point = millimeter.

  • Number of steps between is determined and multiplied accordingly.

  • Final answer: 1 decimeter = 100 millimeters.

Dimensional Analysis

• A method to convert units by multiplying by a conversion factor (in fraction form), which allows for the cancellation of like terms within calculations.

• Example Problem: How many minutes are there in two hours?

  • Given: 1 hour = 60 minutes

  • Calculation: 2 hours × (60 minutes / 1 hour) = 120 minutes

Conversion Factor Explanation

• A conversion factor represents equivalency in fraction form, and enables transitioning from one unit to another while maintaining dimension consistency (e.g., from liters to quarts).

Blood Donation Example Problem

• Determine how many deciliters are in 1 pint of blood given:

  • 2 pints = 1 quart

  • 1.06 quarts = 1 liter

  • 10 deciliters = 1 liter

• Setup: 1 pint × (1 quart / 2 pints) × (1 liter / 1.06 quarts) × (10 deciliters / 1 liter)

• Final Answer: 1 pint = 4.7 deciliters.

Dimensional Analysis Practice Problems

• Convert the following:

  1. 1 foot = _ cm

  2. 3.785 L = _ ounces

  3. 1000 g = _ lbs

  4. 16 ounces = __ kg

  5. 1 mile = _ m

  6. 1 gallon = _ mL

Scientific Notation

• Used for simplifying the expression of large or small numbers:

  • Form: Number × 10^exponent, where the coefficient is between 1 and 10.

  • Examples:

  • 1.23 × 10^-4

  • 5.68 × 10^9

• To write in scientific notation:

  1. Locate the decimal point.

  2. Move the decimal to get a number between 1 and 10.

  3. The number of spaces moved is the exponent; left is positive, right is negative.

Examples of Scientific Notation

1. For 673:

   • Decimal: 673.

   • Move decimal 2 spaces left to get 6.73.

   • Result: 6.73 × 10^2.

2. For 0.0042:

   • Decimal positioning: 0.0042.

   • Move decimal 3 spaces right to get 4.2.

   • Result: 4.2 × 10^-3.

Scientific Notation Practice Problems

• Confirm the following results:

  • 910000 = 9.1 × 10^5

  • 0.00070 = 7.0 × 10^-4

  • 2378.9 = 2.3789 × 10^3

  • 0.000000001 = 1 × 10^-9

  • 53.574 = 5.3574 × 10^1

  • 0.08 = 8 × 10^-2.

Fractions & Scientific Notation

• Some metric prefixes represent fractions of the base unit, which can also be expressed in scientific notation.

• To convert a prefix into scientific notation:

  • Count the zeros in the denominator.

  • This number becomes the negative exponent.

  • Examples:

  • 1/1000 = 1 × 10^-3

  • 1/1,000,000 = 1 × 10^-6