Converting Units of Measurement

Converting units means changing a measurement from one unit to another without changing the actual size or amount. For example, you might measure a desk in inches instead of feet, but the desk stays the exact same length.

To convert between units in the same measurement system, you just need to remember one golden rule:

• Larger unit to smaller unit: Multiply ($\times$)
• Smaller unit to larger unit: Divide ($\div$)

Common Conversion Factors

Before converting, you need to know the basic relationships (conversion factors) between units. Here are a few common ones:

• Length: $1 \text{ foot} = 12 \text{ inches}$
• Weight/Mass: $1 \text{ kilogram} = 1{,}000 \text{ grams}$
• Time: $1 \text{ hour} = 60 \text{ minutes}$

Example 1: Larger to Smaller Unit

Question: Convert $5$ feet to inches.

Solution: Feet are larger than inches, so we are going from a larger unit to a smaller unit. This means we multiply. Since $1 \text{ foot} = 12 \text{ inches}$, we multiply by $12$: $5 \times 12 = 60$ So, $5 \text{ feet} = 60 \text{ inches}$.

Example 2: Smaller to Larger Unit

Question: Convert $3{,}500$ grams to kilograms.

Solution: Grams are smaller than kilograms, so we are going from a smaller unit to a larger unit. This means we divide. Since $1{,}000 \text{ grams} = 1 \text{ kilogram}$, we divide by $1{,}000$: $3{,}500 \div 1{,}000 = 3.5$ So, $3{,}500 \text{ grams} = 3.5 \text{ kilograms}$.

Example 3: Mixed Units

Question: How many minutes are in $3$ hours and $20$ minutes?

Solution: First, convert the hours into minutes. Hours are larger than minutes, so we multiply. Since $1 \text{ hour} = 60 \text{ minutes}$, we multiply by $60$: $3 \times 60 = 180 \text{ minutes}$ Next, add the extra $20$ minutes to the total: $180 + 20 = 200 \text{ minutes}$ So, $3$ hours and $20$ minutes is equal to $200$ minutes.