Lesson 9: Ratio Reasoning: Convert Metric Units

Property

In the metric system, units are related by powers of 10. The prefixes reflect this relationship (e.g., kilo- for 1000, centi- for $\frac{1}{100}$). To convert between metric units, multiply by a conversion factor equal to 1.
Set up the conversion factor as a fraction where: * The desired unit goes in the numerator * The original unit goes in the denominator * The numerical relationship comes from the metric prefixes

Examples

Property

To convert metric units, you can set up a proportion using the known conversion rate and find an equivalent ratio. If the known rate is $\frac{a}{b}$, you can find an equivalent rate by multiplying both the numerator and denominator by the same number, $k$.

Examples

• To convert $5$ meters to centimeters, start with the known rate $\frac{100 \text{ cm}}{1 \text{ m}}$. To find the equivalent amount for $5$ meters, multiply both parts of the ratio by $5$:

So, $5$ meters is equal to $500$ centimeters.

• To convert $3,500$ grams to kilograms, start with the known rate $\frac{1 \text{ kg}}{1000 \text{ g}}$. To find the equivalent amount for $3,500$ grams, multiply both parts of the ratio by $3.5$:

So, $3,500$ grams is equal to $3.5$ kilograms.

• To convert $2.5$ liters to milliliters, start with the known rate $\frac{1000 \text{ mL}}{1 \text{ L}}$. To find the equivalent amount for $2.5$ liters, multiply both parts of the ratio by $2.5$:

So, $2.5$ liters is equal to $2500$ milliliters.

Explanation

This method uses the concept of equivalent ratios to convert between units. First, write the known conversion factor as a rate, such as $\frac{1000 \text{ m}}{1 \text{ km}}$. Then, determine what number you need to multiply the given unit by to get the target unit. Finally, multiply both the numerator and the denominator of the rate by this same number to find the converted measurement.