Lesson 6: Converting Measures

New Concept

Mathematics is the language for describing and solving problems with numbers and quantities. This course builds your foundational skills for mathematical reasoning and problem-solving.

What’s next

To begin, we will apply these skills to convert units of measure. You will see worked examples for length, weight, and capacity.

Property

To convert measures, use the formula:

Examples

• To find how many feet are in a 20-yard rope:
  $$20 \text{ yd} \times 3 \text{ ft per yd} = 60 \text{ ft}$$
• A 3-liter bottle of soda contains:
  $$3 \text{ L} \times 1000 \text{ mL per L} = 3000 \text{ mL}$$
• To convert a 7000-meter race to kilometers:
  $$7000 \text{ m} \div 1000 \text{ m per km} = 7 \text{ km}$$

Explanation

Switching between units is like using a secret code! You just need to multiply or divide by a special number, the 'conversion constant.' It's a magic number that bridges two different measurement worlds, helping you speak both 'yards' and 'feet' fluently.

Property

The symbol

Examples

• An inch is not exactly 2.54 centimeters, but it's very close:
  $$1 \text{ in.} \approx 2.54 \text{ cm}$$
• A mile is roughly one and a half kilometers:
  $$1 \text{ mi} \approx 1.6 \text{ km}$$
• For weight, you can estimate that two pounds is about one kilogram:
  $$2.2 \text{ lb} \approx 1 \text{ kg}$$

Explanation

Sometimes conversions, especially between U.S. and Metric systems, aren't perfectly exact. The

Property

First, convert the larger unit into the smaller unit. Then, add the remaining smaller units to that total.

Examples

• To find the total ounces for a baby weighing 9 pounds, 5 ounces:
  $$(9 \text{ lbs} \times 16 \text{ oz per lb}) + 5 \text{ oz} = 144 \text{ oz} + 5 \text{ oz} = 149 \text{ oz}$$
• To find the height in inches of someone who is 5 feet 10 inches tall:
  $$(5 \text{ ft} \times 12 \text{ in. per ft}) + 10 \text{ in.} = 60 \text{ in.} + 10 \text{ in.} = 70 \text{ in.}$$

Explanation

Think of this as a two-part quest! First, you tackle the main challenge by converting the big units into smaller ones. Then, you scoop up any leftover small units and add them to your treasure. It’s a powerful combo move for mixed measurements!