Solved Exercises on Conversions within the Same System (Metric & Customary) in Grade 3

Master unit conversions: metric system (centimeters, meters, kilometers) and customary system (inches, feet, yards) through these 5 detailed exercises with step-by-step solutions.

Solution: Exercises 1 to 3
1 Metric length conversion
Exercise 1
Convert 3 meters to centimeters. Show your work step by step.
Definition:

Metric system: A measurement system based on powers of 10. In length: 1 meter = 100 centimeters

Conversion method:
  1. Identify the conversion factor: 1 meter = 100 centimeters
  2. Multiply the number of meters by 100
  3. Express the result in centimeters
Starting amount
3 meters
Conversion factor
× 100
Result
300 cm
Step 1: Identify the conversion factor

1 meter = 100 centimeters

Step 2: Set up the multiplication

3 meters × 100 centimeters per meter

Step 3: Perform the calculation

3 × 100 = 300

Step 4: Write the final answer

3 meters = 300 centimeters

3 m = 300 cm
Final answer:

3 meters equals 300 centimeters

Applied rules:

• Conversion factor: 1 m = 100 cm

• Multiplication: To convert from larger unit to smaller unit, multiply

• Metric system: Based on powers of 10

2 Metric liquid volume conversion
Exercise 2
Convert 4 liters to milliliters. Show your work step by step.
Definition:

Liquid volume: Amount of liquid measured in liters (L) or milliliters (mL)

Starting amount
4 liters
Conversion factor
× 1,000
Result
4,000 mL
Step 1: Identify the conversion factor

1 liter = 1,000 milliliters

Step 2: Set up the multiplication

4 liters × 1,000 milliliters per liter

Step 3: Perform the calculation

4 × 1,000 = 4,000

Step 4: Write the final answer

4 liters = 4,000 milliliters

4 L = 4,000 mL
Final answer:

4 liters equals 4,000 milliliters

Applied rules:

• Conversion factor: 1 L = 1,000 mL

• Multiplication: To convert from larger unit to smaller unit, multiply

• Metric system: Based on powers of 10

3 Metric weight conversion
Exercise 3
Convert 5,000 grams to kilograms. Show your work step by step.
Definition:

Weight/Mass: Amount of matter measured in grams (g) or kilograms (kg)

Starting amount
5,000 grams
Conversion factor
÷ 1,000
Result
5 kg
Step 1: Identify the conversion factor

1 kilogram = 1,000 grams

Step 2: Set up the division

5,000 grams ÷ 1,000 grams per kilogram

Step 3: Perform the calculation

5,000 ÷ 1,000 = 5

Step 4: Write the final answer

5,000 grams = 5 kilograms

5,000 g = 5 kg
Final answer:

5,000 grams equals 5 kilograms

Applied rules:

• Conversion factor: 1 kg = 1,000 g

• Division: To convert from smaller unit to larger unit, divide

• Metric system: Based on powers of 10

Key Concepts: Metric & Customary Systems
1 m = 100 cm
Metric Length
1 L = 1,000 mL
Metric Volume
1 kg = 1,000 g
Metric Weight
Metric System
Powers of 10
Based on 10, 100, 1,000...
Customary System
Different Factors
Uses various conversion factors
Conversion Rule
Multiply/Divide
Smaller→Larger: divide, Larger→Smaller: multiply
Key definitions:

Metric system: A decimal-based measurement system used worldwide. Units are related by powers of 10.

Customary system: A measurement system used primarily in the United States. Units have irregular relationships.

Conversion: Changing from one unit of measurement to another equivalent unit.

Conversion factor: The ratio used to convert between units.

Complete methodology:
  1. Identify units: Determine the starting unit and the target unit
  2. Find conversion factor: Know the relationship between the units
  3. Choose operation: Multiply when going from larger to smaller units, divide when going from smaller to larger
  4. Calculate: Perform the multiplication or division
  5. Check: Verify the answer makes sense
Tip 1: Remember: "King Henry Died By Drinking Chocolate Milk" for metric prefixes (Kilo, Hecto, Deka, Base, Deci, Centi, Milli).
Tip 2: When converting to a smaller unit, the number gets bigger (multiply).
Tip 3: When converting to a larger unit, the number gets smaller (divide).
Tip 4: Always include the correct units in your final answer.
Metric relationships: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 L = 1,000 mL, 1 kg = 1,000 g.
Customary relationships: 1 foot = 12 inches, 1 yard = 3 feet, 1 mile = 1,760 yards, 1 pound = 16 ounces.
Essential conversion rules:

• Metric length: 1 m = 100 cm, 1 km = 1,000 m

• Metric volume: 1 L = 1,000 mL

• Metric weight: 1 kg = 1,000 g

• To convert larger → smaller: multiply

• To convert smaller → larger: divide

Solution: Exercises 4 to 5
4 Customary length conversion
Exercise 4
Convert 3 feet to inches. Show your work step by step.
Definition:

Customary system: Measurement system used in the US. For length: 1 foot = 12 inches

Starting amount
3 feet
Conversion factor
× 12
Result
36 inches
Step 1: Identify the conversion factor

1 foot = 12 inches

Step 2: Set up the multiplication

3 feet × 12 inches per foot

Step 3: Perform the calculation

3 × 12 = 36

Step 4: Write the final answer

3 feet = 36 inches

3 ft = 36 in
Final answer:

3 feet equals 36 inches

Applied rules:

• Conversion factor: 1 ft = 12 in

• Multiplication: To convert from larger unit to smaller unit, multiply

• Customary system: Irregular relationships between units

5 Customary weight conversion
Exercise 5
Convert 4 pounds to ounces. Show your work step by step.
Definition:

Customary weight: Measurement system for weight in the US. 1 pound = 16 ounces

Starting amount
4 pounds
Conversion factor
× 16
Result
64 ounces
Step 1: Identify the conversion factor

1 pound = 16 ounces

Step 2: Set up the multiplication

4 pounds × 16 ounces per pound

Step 3: Perform the calculation

4 × 16 = 64

Step 4: Write the final answer

4 pounds = 64 ounces

4 lb = 64 oz
Final answer:

4 pounds equals 64 ounces

Applied rules:

• Conversion factor: 1 lb = 16 oz

• Multiplication: To convert from larger unit to smaller unit, multiply

• Customary system: Irregular relationships between units

Complete Guide: Metric & Customary Systems
1 m = 100 cm
Metric Length Conversion
Key definitions:

Metric system: A decimal-based measurement system where units are related by powers of 10. Used worldwide in science and most countries.

Customary system: A measurement system primarily used in the United States, with irregular relationships between units.

Conversion: The process of changing from one unit of measurement to another equivalent unit within the same system.

Base units: Fundamental units in the metric system (meter for length, liter for volume, gram for mass).

Complete conversion methodology:
  1. Identify the starting unit: What unit are you converting from?
  2. Identify the target unit: What unit are you converting to?
  3. Determine the conversion factor: What is the relationship between the units?
  4. Choose the operation: Multiply when going from larger to smaller units, divide when going from smaller to larger
  5. Perform the calculation: Carry out the multiplication or division
  6. Express the answer: Include the correct units
  7. Verify: Check if the answer makes sense
Tip 1: The metric system is easier because it's based on 10: 10, 100, 1,000, etc.
Tip 2: In metric, move the decimal point: 3 meters = 300 centimeters (move 2 places right).
Tip 3: Remember: "Smaller unit, bigger number" and "Bigger unit, smaller number".
Tip 4: Practice with real objects: measure your desk in feet and inches, then convert.
Metric system advantages: Consistent base-10 relationships, easy to learn, used internationally.
Common mistakes: Confusing conversion factors, using wrong operation, forgetting units.
Essential conversion rules:

• Metric length: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm

• Metric volume: 1 L = 1,000 mL

• Metric weight: 1 kg = 1,000 g

• Customary length: 1 foot = 12 inches, 1 yard = 3 feet

• Customary weight: 1 pound = 16 ounces

• Direction rule: Larger → smaller: multiply; Smaller → larger: divide

Questions & Answers

Question: Why do we have two different measurement systems? Why can't we just use one?

Answer: Different systems developed in different parts of the world over centuries:

  • Metric system: Created in France in the 1700s, designed to be logical and based on 10
  • Customary system: Developed in England and brought to America, based on older traditional measures

Most countries now use the metric system because it's easier to work with (based on 10s). The US still uses customary units in daily life, but even in the US, scientists and medicine use the metric system. Learning both helps you communicate with people everywhere!

Question: How do I remember all these different conversion factors? They seem so hard to remember!

Answer: Focus on the most common ones and use memory tricks:

  • For metric: Just remember "kilo" means thousand, so 1 kg = 1,000 g, 1 km = 1,000 m, 1 L = 1,000 mL
  • For length: Remember: 1 foot = 12 inches (like 12 months in a year), 1 yard = 3 feet (like 3 little pigs)
  • For weight: Remember: 1 pound = 16 ounces (like 16 candles on a birthday cake)

Practice with real objects - measure things around your house to build familiarity with the units!

Question: When I convert from a bigger unit to a smaller unit, why does the number get bigger?

Answer: Think of it this way: it takes MORE small pieces to make up a big piece!

  • 1 meter is a big unit, but it takes 100 centimeters (smaller units) to equal that 1 meter
  • 1 dollar is a big unit, but it takes 100 pennies (smaller units) to equal that 1 dollar
  • 1 pizza is a big unit, but it takes 8 slices (smaller units) to equal that 1 pizza

So when you convert from a bigger unit to a smaller unit, you're counting how many of the smaller pieces fit into the bigger piece - that's why the number gets bigger!