Metric Units of Measurement - Fifth Grade
Complete Notes & Formulas
Understanding the Metric System
What is the Metric System?
The metric system (also called SI - International System of Units) is a decimal-based measurement system used worldwide. It's based on powers of 10, making conversions easy!
Metric Prefixes
| Prefix | Symbol | Meaning | Power of 10 |
|---|---|---|---|
| kilo- | k | 1,000 times | 10³ |
| hecto- | h | 100 times | 10² |
| deca- | da | 10 times | 10¹ |
| BASE UNIT | — | 1 | 10⁰ |
| deci- | d | 1/10 | 10⁻¹ |
| centi- | c | 1/100 | 10⁻² |
| milli- | m | 1/1,000 | 10⁻³ |
The Golden Rule of Metric Conversions
LARGER Unit → SMALLER Unit: MULTIPLY by powers of 10
SMALLER Unit → LARGER Unit: DIVIDE by powers of 10
1. Compare and Convert Metric Units of Length
Metric Units of Length
| Unit | Symbol | Used For |
|---|---|---|
| Kilometer | km | Long distances (roads, cities) |
| Meter | m | Medium lengths (room, height) |
| Centimeter | cm | Small lengths (pencil, hand) |
| Millimeter | mm | Very small lengths (thickness) |
Length Conversion Formulas
1 kilometer (km) = 1,000 meters (m)
1 meter (m) = 100 centimeters (cm)
1 centimeter (cm) = 10 millimeters (mm)
Quick Reference:
1 m = 1,000 mm
1 km = 100,000 cm
Examples
Example 1: Convert 5 kilometers to meters
• Larger to smaller → Multiply
• 1 km = 1,000 m
• 5 × 1,000 = 5,000 meters
Example 2: Convert 350 centimeters to meters
• Smaller to larger → Divide
• 1 m = 100 cm
• 350 ÷ 100 = 3.5 meters
Example 3: Compare: 7 m ___ 650 cm
• Convert to same unit (cm): 7 m = 7 × 100 = 700 cm
• 700 cm vs 650 cm
• Answer: 7 m > 650 cm
2. Compare and Convert Metric Units of Mass
Metric Units of Mass
| Unit | Symbol | Used For |
|---|---|---|
| Kilogram | kg | Heavy objects (person, bag) |
| Gram | g | Light objects (apple, paper) |
| Milligram | mg | Very light (medicine, salt grain) |
Mass Conversion Formulas
1 kilogram (kg) = 1,000 grams (g)
1 gram (g) = 1,000 milligrams (mg)
Quick Reference:
1 kg = 1,000,000 mg
Examples
Example 1: Convert 3 kilograms to grams
• Larger to smaller → Multiply
• 1 kg = 1,000 g
• 3 × 1,000 = 3,000 grams
Example 2: Convert 7,500 grams to kilograms
• Smaller to larger → Divide
• 1 kg = 1,000 g
• 7,500 ÷ 1,000 = 7.5 kilograms
Example 3: Convert 4 grams to milligrams
• Larger to smaller → Multiply
• 1 g = 1,000 mg
• 4 × 1,000 = 4,000 milligrams
3. Compare and Convert Metric Units of Volume
Metric Units of Volume (Capacity)
| Unit | Symbol | Used For |
|---|---|---|
| Liter | L | Large volumes (bottles, jugs) |
| Milliliter | mL | Small volumes (spoon, medicine) |
Volume Conversion Formula
1 liter (L) = 1,000 milliliters (mL)
Important Note
Fun Fact: 1 milliliter (mL) = 1 cubic centimeter (cm³). They measure the same volume!
Examples
Example 1: Convert 6 liters to milliliters
• Larger to smaller → Multiply
• 1 L = 1,000 mL
• 6 × 1,000 = 6,000 milliliters
Example 2: Convert 2,500 milliliters to liters
• Smaller to larger → Divide
• 1 L = 1,000 mL
• 2,500 ÷ 1,000 = 2.5 liters
4. Conversion Tables - Metric Units
Complete Metric Conversion Reference
LENGTH CONVERSIONS
| 1 kilometer (km) | = | 1,000 meters (m) |
| 1 meter (m) | = | 100 centimeters (cm) |
| 1 meter (m) | = | 1,000 millimeters (mm) |
| 1 centimeter (cm) | = | 10 millimeters (mm) |
MASS CONVERSIONS
| 1 kilogram (kg) | = | 1,000 grams (g) |
| 1 gram (g) | = | 1,000 milligrams (mg) |
VOLUME CONVERSIONS
| 1 liter (L) | = | 1,000 milliliters (mL) |
5. Convert Metric Mixed Units
What are Mixed Units?
Mixed units combine two metric units together, like 5 km 200 m or 2 L 350 mL.
Two Types of Conversion
Type 1: Mixed Units → Single Unit
Steps:
1. Convert the larger unit to the smaller unit
2. Add the remaining smaller units
Type 2: Single Unit → Mixed Units
Steps:
1. Divide to find the larger unit
2. The remainder is the smaller unit
Examples
Example 1: Convert 3 km 750 m to meters
Step 1: Convert km to m
3 km × 1,000 = 3,000 m
Step 2: Add the remaining meters
3,000 + 750 = 3,750 meters
Example 2: Convert 5,600 grams to kg and g
Step 1: Divide by 1,000
5,600 ÷ 1,000 = 5 remainder 600
Step 2: Write as mixed units
5 kg 600 g
Example 3: Convert 2 L 475 mL to milliliters
• 2 L × 1,000 = 2,000 mL
• 2,000 + 475 = 2,475 milliliters
6. Add and Subtract Metric Mixed Units
Steps to Add Mixed Units
Step 1: Add the larger units together
Step 2: Add the smaller units together
Step 3: If smaller units ≥ 1,000, convert to larger unit
Step 4: Simplify the answer
Steps to Subtract Mixed Units
Step 1: If you can't subtract smaller units, borrow from larger unit
Step 2: Subtract the smaller units
Step 3: Subtract the larger units
Examples
Addition Example: Add 4 m 750 cm + 2 m 450 cm
Step 1: Add meters: 4 + 2 = 6 m
Step 2: Add centimeters: 750 + 450 = 1,200 cm
Step 3: 1,200 cm = 12 m (since 100 cm = 1 m)
Step 4: 6 m + 12 m = 18 m
Answer: 18 m (or 1,800 cm)
Subtraction Example: Subtract 5 L 200 mL - 2 L 600 mL
Problem: Can't subtract 600 mL from 200 mL
Step 1: Borrow 1 L = 1,000 mL from 5 L
5 L 200 mL becomes 4 L 1,200 mL
Step 2: Now subtract mL: 1,200 - 600 = 600 mL
Step 3: Subtract L: 4 - 2 = 2 L
Answer: 2 L 600 mL
7. Multi-Step Problems with Metric Unit Conversions
What are Multi-Step Problems?
These problems require multiple conversions and operations (add, subtract, multiply, divide) to solve.
Strategy
Step 1: Read the problem carefully
Step 2: Identify what you need to find
Step 3: Convert all measurements to the same unit
Step 4: Perform the necessary operations
Step 5: Convert back if needed
Step 6: Check if your answer makes sense
Examples
"A water tank holds 8 liters. If 2,500 milliliters are used, how many milliliters remain?"
Step 1: Convert liters to milliliters
8 L × 1,000 = 8,000 mL
Step 2: Subtract amount used
8,000 - 2,500 = 5,500 mL
Answer: 5,500 milliliters remain
"Maria walks 2 km to school each day. How many meters does she walk in 5 days?"
Step 1: Convert km to meters
2 km × 1,000 = 2,000 m per day
Step 2: Multiply by 5 days
2,000 × 5 = 10,000 m
Answer: Maria walks 10,000 meters (or 10 km) in 5 days
"A bag contains 4,500 grams of flour. If a baker uses 2 kg, how many grams are left?"
Step 1: Convert kg to grams
2 kg × 1,000 = 2,000 g
Step 2: Subtract from total
4,500 - 2,000 = 2,500 g
Answer: 2,500 grams (or 2.5 kg) are left
8. Multi-Step Problems: Customary or Metric Unit Conversions
Key Difference
Some problems may ask you to choose the appropriate measurement system or convert between customary and metric units.
Approximate Conversions (Optional Reference)
• 1 inch ≈ 2.54 centimeters
• 1 mile ≈ 1.6 kilometers
• 1 pound ≈ 454 grams
• 1 quart ≈ 0.95 liters
Strategy
Always identify which measurement system the problem is using, and stay consistent within that system unless asked to convert.
Example
"Tom bought 3 meters of fabric. Sarah bought 250 centimeters. Who bought more fabric and by how much?"
Step 1: Convert to same unit (cm)
Tom: 3 m × 100 = 300 cm
Sarah: 250 cm
Step 2: Compare
300 cm > 250 cm
Step 3: Find difference
300 - 250 = 50 cm
Answer: Tom bought more fabric by 50 cm (or 0.5 m)
Complete Metric Conversion Chart
LENGTH
1 km = 1,000 m
1 m = 100 cm
1 cm = 10 mm
1 m = 1,000 mm
MASS
1 kg = 1,000 g
1 g = 1,000 mg
1 kg = 1,000,000 mg
VOLUME
1 L = 1,000 mL
1 mL = 1 cm³
💡 Important Tips to Remember
✓ The metric system is based on powers of 10 - everything multiplies/divides by 10, 100, or 1,000
✓ MULTIPLY when converting from LARGER to SMALLER units
✓ DIVIDE when converting from SMALLER to LARGER units
✓ Memorize the basic conversions: 1,000 (kilo), 100 (centi), 10 (milli)
✓ The prefix kilo- always means 1,000
✓ The prefix centi- always means 1/100 (think: cent = 1/100 of a dollar)
✓ The prefix milli- always means 1/1,000
✓ Always convert to the same unit before comparing
✓ Include correct units in your final answer
🧠 Memory Tricks for Metric System
King Henry Died By Drinking Chocolate Milk
King = Kilo
Henry = Hecto
Died = Deca
By = BASE UNIT (meter, gram, liter)
Drinking = Deci
Chocolate = Centi
Milk = Milli
Counting Zeros Trick:
• Kilo = 3 zeros (1,000)
• Hecto = 2 zeros (100)
• Deca = 1 zero (10)
Movement Trick:
When you move RIGHT on the chart (larger to smaller), move the decimal point RIGHT
When you move LEFT on the chart (smaller to larger), move the decimal point LEFT
Master the Metric System! 📏⚖️🥤
The metric system is used worldwide - practice conversions daily!