Converting Metric Units

The metric system is a base-10 measurement system. This makes converting between different units incredibly easy! All you have to do is multiply or divide by powers of 10, such as $10$, $100$, or $1{,}000$.

The Golden Rule of Conversion

To successfully convert metric units, remember this simple rule:

• Large to Small: Multiply (because you will need more of the smaller unit to make up the same amount).
• Small to Large: Divide (because you will need fewer of the larger unit).

Key Metric Relationships

Here are the standard conversions you need to know for length, mass, and capacity:

Length

• $1 \text{ kilometer (km)} = 1{,}000 \text{ meters (m)}$
• $1 \text{ meter (m)} = 100 \text{ centimeters (cm)}$
• $1 \text{ centimeter (cm)} = 10 \text{ millimeters (mm)}$

Mass

• $1 \text{ kilogram (kg)} = 1{,}000 \text{ grams (g)}$
• $1 \text{ gram (g)} = 1{,}000 \text{ milligrams (mg)}$

Capacity

• $1 \text{ liter (L)} = 1{,}000 \text{ milliliters (mL)}$

Example Problems

Example 1: Convert $3.5 \text{ km}$ to meters.

• Step 1: Identify the direction. We are going from kilometers (large) to meters (small), so we multiply.
• Step 2: Find the conversion factor. There are $1{,}000 \text{ m}$ in $1 \text{ km}$.
• Step 3: Calculate. $3.5 \times 1{,}000 = 3{,}500$
• Answer: $3.5 \text{ km} = 3{,}500 \text{ m}$

Example 2: Convert $2{,}500 \text{ mL}$ to liters.

• Step 1: Identify the direction. We are going from milliliters (small) to liters (large), so we divide.
• Step 2: Find the conversion factor. There are $1{,}000 \text{ mL}$ in $1 \text{ L}$.
• Step 3: Calculate. $2{,}500 \div 1{,}000 = 2.5$
• Answer: $2{,}500 \text{ mL} = 2.5 \text{ L}$

Example 3: A recipe needs $0.75 \text{ kg}$ of flour. How many grams is that?

• Step 1: We are converting kilograms to grams (large to small), so we multiply.
• Step 2: There are $1{,}000 \text{ g}$ in $1 \text{ kg}$.
• Step 3: Calculate. $0.75 \times 1{,}000 = 750$
• Answer: The recipe needs $750 \text{ g}$ of flour.