Applied Math for Nurses: Metric Unit Conversions Using The Line

Purpose and Overview of Metric Conversion

• Converting between metric units requires sliding the decimal point by a specific number of places in the appropriate direction.

• Metric conversion relies on a structured mnemonic framework called "The Line" to remember the order of metric units and the exact number of decimal shifts required.

The King Henry Mnemonic and Metric Chart Structure

• The mnemonic sentence used to remember the ordering and relative values of metric prefixes is:   "KING HENRY’S DAUGHTER USUALLY DOESN’T COOK MUCH X X MERCI"

• Breakdown of each element in the mnemonic, including symbol, full name, and associated unit prefix:

  • KING:

  • Symbol: $\text{K}$

  • Name: Kilo

  • Prefix / Unit: $\text{kg}$

  • HENRY’S:

  • Symbol: $\text{H}$

  • Name: Hecto

  • Prefix / Unit: $\text{h}$

  • DAUGHTER:

  • Symbol: $\text{D}$

  • Name: Deca

  • Prefix / Unit: $\text{da}$

  • USUALLY:

  • Symbol: $\text{U}$

  • Name: Usually Unit

  • Prefix / Unit: $\text{G}$, $\text{M}$, $\text{L}$ (representing Grams, Meters, or Liters)

  • DOESN’T:

  • Symbol: $\text{D}$

  • Name: Deci

  • Prefix / Unit: Standard decimal fraction

  • COOK:

  • Symbol: $\text{C}$

  • Name: Centi

  • Prefix / Unit: $\text{c}$

  • MUCH:

  • Symbol: $\text{M}$

  • Name: Milli

  • Prefix / Unit: $\text{mg}$

  • X:

  • Symbol: $\text{X}$

  • Name: Placeholder

  • Prefix / Unit: None ($-\text{--}$)

  • X:

  • Symbol: $\text{X}$

  • Name: Placeholder

  • Prefix / Unit: None ($-\text{--}$)

  • MERCI:

  • Symbol: $\text{M}$

  • Name: Micro

  • Prefix / Unit: $\text{mcg}$

Step-by-Step Instructions for Constructing "The Line"

• Step 1: Draw a horizontal line across the page.

• Step 2: Draw a perpendicular line in the center of the horizontal line.

• Step 3: Label the center perpendicular line as "Usually" (for base units), which represents grams ($\text{g}$), meters ($\text{m}$), or liters ($\text{L}$).

• Step 4: Divide the left side of the horizontal line into $3$ equal parts.

• Step 5: Label each division point on the left side from left to right with the prefixes:

  • Kilo

  • Hecto

  • Deca

• Step 6: Divide the right side of the horizontal line into $6$ equal parts.

• Step 7: Label each division point on the right side from left to right with the prefixes and placeholders:

  • Deci

  • Centi

  • Milli

  • $\text{X}$

  • $\text{X}$

  • Micro

Principles of Metric Unit Conversion

• Metric unit conversion using the "King Henry" method involves identifying the starting unit location and sliding the decimal point to the target unit location.

• Zeros are inserted into any empty decimal places created during the shift.

• Directional Rules for Decimal Movement:

  • Moving the decimal to the right corresponds to multiplication.

  • Moving the decimal to the left corresponds to division.

Worked Examples of Metric Conversions

• Example 1: Converting $23\,\text{g}$ to Milligrams ($\text{mg}$)

  • Goal: Convert $23\,\text{g}$ to $\text{mg}$.

  • Step 1 (Starting Position): Locate the starting unit of grams ($\text{g}$) at $\text{U}$ ("Usually").

  • Step 2 (Target Position): Locate the ending position at $\text{mg}$ ("Much").

  • Step 3 (Determine Movement):

  • Visual sequence: $\text{K} \quad \text{H} \quad \text{D} \quad \text{U} \quad \text{D} \quad \text{C} \quad \text{M} \quad \text{X} \quad \text{X} \quad \text{M}$

  • Sliding from $\text{U}$ to $\text{M}$ requires moving $3$ decimal places to the right.

  • Moving to the right indicates multiplying by $10^3 = 1000$.

  • Calculation and Decimal Movement:

  • $23 \rightarrow 230 \rightarrow 2300 \rightarrow 23000$

  • $23\,\text{g} = 23000\,\text{mg}$

• Example 2: Converting $3\,\text{mcg}$ to Milligrams ($\text{mg}$)

  • Goal: Convert $3\,\text{mcg}$ to $\text{mg}$.

  • Step 1 (Starting Position): Locate the starting unit of micrograms ($\text{mcg}$) at $\text{M}$ ("Merci").

  • Step 2 (Target Position): Locate the ending position at milligrams ($\text{mg}$) at $\text{M}$ ("Much").

  • Step 3 (Determine Movement):

  • Visual sequence: $\text{K} \quad \text{H} \quad \text{D} \quad \text{U} \quad \text{D} \quad \text{C} \quad \text{M} \quad \text{X} \quad \text{X} \quad \text{M}$

  • Sliding from "Merci" ($\text{mcg}$) to "Much" ($\text{mg}$) across the two $\text{X}$ placeholders requires moving $3$ decimal places to the left.

  • Moving to the left indicates dividing by $10^3 = 1000$.

  • Calculation and Decimal Movement:

  • $3\,\text{mcg} \rightarrow 0.3 \rightarrow 0.03 \rightarrow 0.003$

  • $3\,\text{mcg} = 0.003\,\text{mg}$