📐 Metric Units of Measurement - Complete Notes & Formulas 📊
🎯 THE METRIC SYSTEM ADVANTAGE 🎯
BASE 10 SYSTEM - Everything is × or ÷ by 10, 100, 1000!
LARGER → SMALLER: MULTIPLY (×)
SMALLER → LARGER: DIVIDE (÷)
🪜 THE METRIC LADDER - King Henry Died By Drinking Chocolate Milk
Each step = × or ÷ by 10 | Move decimal point one place per step!
1. Compare and Convert Metric Units of Length
📏 Metric Units of Length:
| Unit | Symbol | Conversion to Meters |
|---|---|---|
| Millimeter | mm | 1 mm = 0.001 m |
| Centimeter | cm | 1 cm = 0.01 m |
| Meter (Base Unit) | m | 1 m = 1 m |
| Kilometer | km | 1 km = 1,000 m |
1 centimeter = 10 millimeters
1 meter = 100 centimeters = 1,000 millimeters
1 kilometer = 1,000 meters = 100,000 cm = 1,000,000 mm
Converting Larger to Smaller (MULTIPLY):
Example 1: Convert 5 meters to centimeters
1 Identify: Meters → Centimeters (larger to smaller)
2 Count ladder steps: m to cm = 2 steps down
3 Formula: Meters × 100 = Centimeters
4 Calculate: 5 × 100 = 500 centimeters
Example 2: Convert 3 kilometers to meters
Solution: 3 km × 1,000 = 3,000 meters
Example 3: Convert 8 centimeters to millimeters
Solution: 8 cm × 10 = 80 millimeters
Converting Smaller to Larger (DIVIDE):
Example 4: Convert 4,000 meters to kilometers
1 Identify: Meters → Kilometers (smaller to larger)
2 Count ladder steps: m to km = 3 steps up
3 Formula: Meters ÷ 1,000 = Kilometers
4 Calculate: 4,000 ÷ 1,000 = 4 kilometers
Example 5: Convert 250 centimeters to meters
Solution: 250 cm ÷ 100 = 2.5 meters
Comparing Lengths:
Example 6: Which is longer: 3 meters or 250 centimeters?
Solution: Convert to the same unit:
3 meters = 3 × 100 = 300 centimeters
Compare: 300 cm > 250 cm
Answer: 3 meters is longer
- Use the ladder method: Count steps and move decimal point
- km → m → cm → mm (going down = multiply by 10, 100, 1000)
- mm → cm → m → km (going up = divide by 10, 100, 1000)
- 1 meter ≈ 3 feet (slightly longer)
- 1 kilometer ≈ 0.6 miles
2. Compare and Convert Metric Units of Mass
⚖️ Metric Units of Mass (Weight):
| Unit | Symbol | Conversion to Grams |
|---|---|---|
| Milligram | mg | 1 mg = 0.001 g |
| Gram (Base Unit) | g | 1 g = 1 g |
| Kilogram | kg | 1 kg = 1,000 g |
| Metric Ton | t | 1 t = 1,000,000 g |
1 gram = 1,000 milligrams
1 kilogram = 1,000 grams = 1,000,000 mg
1 metric ton = 1,000 kilograms = 1,000,000 grams
Converting Larger to Smaller (MULTIPLY):
Example 1: Convert 7 kilograms to grams
1 Identify: Kilograms → Grams (larger to smaller)
2 Count ladder steps: kg to g = 3 steps down
3 Formula: Kilograms × 1,000 = Grams
4 Calculate: 7 × 1,000 = 7,000 grams
Example 2: Convert 4 grams to milligrams
Solution: 4 g × 1,000 = 4,000 milligrams
Example 3: Convert 2.5 kilograms to grams
Solution: 2.5 kg × 1,000 = 2,500 grams
Converting Smaller to Larger (DIVIDE):
Example 4: Convert 6,000 grams to kilograms
1 Identify: Grams → Kilograms (smaller to larger)
2 Count ladder steps: g to kg = 3 steps up
3 Formula: Grams ÷ 1,000 = Kilograms
4 Calculate: 6,000 ÷ 1,000 = 6 kilograms
Example 5: Convert 8,000 milligrams to grams
Solution: 8,000 mg ÷ 1,000 = 8 grams
Comparing Masses:
Example 6: Which is heavier: 2,500 grams or 3 kilograms?
Solution: Convert to the same unit:
3 kilograms = 3 × 1,000 = 3,000 grams
Compare: 2,500 grams < 3,000 grams
Answer: 3 kilograms is heavier
- kg → g → mg (going down = multiply by 1,000)
- mg → g → kg (going up = divide by 1,000)
- 1 kilogram ≈ 2.2 pounds
- Mass and weight are different, but we often use them interchangeably
- Remember: kilo = 1,000 (like kilometer!)
3. Compare and Convert Metric Units of Volume
🥤 Metric Units of Volume (Capacity):
| Unit | Symbol | Conversion to Liters |
|---|---|---|
| Milliliter | mL | 1 mL = 0.001 L |
| Centiliter | cL | 1 cL = 0.01 L |
| Liter (Base Unit) | L | 1 L = 1 L |
| Kiloliter | kL | 1 kL = 1,000 L |
1 liter = 1,000 milliliters
1 liter = 100 centiliters
1 kiloliter = 1,000 liters = 1,000,000 milliliters
Special Relationship:
This connects volume and length measurements!
Converting Larger to Smaller (MULTIPLY):
Example 1: Convert 6 liters to milliliters
1 Identify: Liters → Milliliters (larger to smaller)
2 Count ladder steps: L to mL = 3 steps down
3 Formula: Liters × 1,000 = Milliliters
4 Calculate: 6 × 1,000 = 6,000 milliliters
Example 2: Convert 3.5 liters to milliliters
Solution: 3.5 L × 1,000 = 3,500 milliliters
Example 3: Convert 2 kiloliters to liters
Solution: 2 kL × 1,000 = 2,000 liters
Converting Smaller to Larger (DIVIDE):
Example 4: Convert 9,000 milliliters to liters
1 Identify: Milliliters → Liters (smaller to larger)
2 Count ladder steps: mL to L = 3 steps up
3 Formula: Milliliters ÷ 1,000 = Liters
4 Calculate: 9,000 ÷ 1,000 = 9 liters
Example 5: Convert 500 milliliters to liters
Solution: 500 mL ÷ 1,000 = 0.5 liters
Comparing Volumes:
Example 6: Which is more: 4 liters or 3,500 milliliters?
Solution: Convert to the same unit:
4 liters = 4 × 1,000 = 4,000 milliliters
Compare: 4,000 mL > 3,500 mL
Answer: 4 liters is more
- kL → L → mL (going down = multiply by 1,000)
- mL → L → kL (going up = divide by 1,000)
- 1 liter ≈ 1 quart (slightly more)
- 1 liter of water weighs 1 kilogram!
- Use mL for small amounts (medicine, cooking)
- Use L for larger amounts (bottles, containers)
4. Compare and Convert All Metric Units
1 Identify which measurement type (length, mass, or volume)
2 Convert both measurements to the SAME unit
3 Use the ladder method: count steps and move decimal
4 Compare the numbers
Mixed Unit Type Comparisons:
Example 1 - Length: Compare: 800 centimeters __ 9 meters
Solution:
Convert 9 meters to centimeters: 9 × 100 = 900 cm
Compare: 800 cm < 900 cm
Answer: 800 centimeters < 9 meters
Example 2 - Mass: Compare: 5,200 grams __ 5 kilograms
Solution:
Convert 5 kilograms to grams: 5 × 1,000 = 5,000 grams
Compare: 5,200 g > 5,000 g
Answer: 5,200 grams > 5 kilograms
Example 3 - Volume: Compare: 2 liters __ 2,000 milliliters
Solution:
Convert 2 liters to milliliters: 2 × 1,000 = 2,000 mL
Compare: 2,000 mL = 2,000 mL
Answer: 2 liters = 2,000 milliliters
📊 Complete Metric Conversion Chart
| Measurement Type | Base Unit | Common Conversions |
|---|---|---|
| Length | Meter (m) | 1 km = 1,000 m | 1 m = 100 cm | 1 cm = 10 mm |
| Mass | Gram (g) | 1 kg = 1,000 g | 1 g = 1,000 mg |
| Volume | Liter (L) | 1 kL = 1,000 L | 1 L = 1,000 mL |
5. Conversion Tables - Metric Units
How to Complete Conversion Tables:
Example 1: Complete this conversion table for meters and centimeters
| Meters | Centimeters |
|---|---|
| 1 | 100 |
| 2 | 200 |
| 3 | 300 |
| 4 | 400 |
| 5 | 500 |
Pattern: Each meter equals 100 centimeters, so multiply meters by 100!
Example 2: Complete this conversion table for kilograms and grams
| Kilograms | Grams |
|---|---|
| 1 | 1,000 |
| 2 | 2,000 |
| 3 | 3,000 |
| 4 | 4,000 |
| 5 | 5,000 |
Pattern: Each kilogram equals 1,000 grams, so multiply kilograms by 1,000!
Example 3: Complete this conversion table for liters and milliliters
| Liters | Milliliters |
|---|---|
| 0.5 | 500 |
| 1 | 1,000 |
| 1.5 | 1,500 |
| 2 | 2,000 |
| 2.5 | 2,500 |
Pattern: Each liter equals 1,000 milliliters, so multiply liters by 1,000!
- Look for the multiplication pattern (×10, ×100, ×1000)
- Each row shows equivalent measurements
- Use the pattern to fill in missing values
- Check your work by converting back
- Metric tables always use base 10 patterns!
6. Convert Metric Mixed Units
Converting Mixed Units to Single Units:
Example 1: Convert 3 meters 45 centimeters to centimeters
Solution:
1 Convert meters: 3 × 100 = 300 centimeters
2 Add remaining centimeters: 300 + 45 = 345 centimeters
Example 2: Convert 5 kilograms 250 grams to grams
Solution:
1 Convert kilograms: 5 × 1,000 = 5,000 grams
2 Add remaining grams: 5,000 + 250 = 5,250 grams
Example 3: Convert 7 liters 600 milliliters to milliliters
Solution:
1 Convert liters: 7 × 1,000 = 7,000 milliliters
2 Add remaining milliliters: 7,000 + 600 = 7,600 milliliters
Converting Single Units to Mixed Units:
Example 4: Convert 475 centimeters to meters and centimeters
Solution:
1 Divide: 475 ÷ 100 = 4 remainder 75
2 Write: 4 meters 75 centimeters
Example 5: Convert 3,750 grams to kilograms and grams
Solution:
1 Divide: 3,750 ÷ 1,000 = 3 remainder 750
2 Write: 3 kilograms 750 grams
Example 6: Convert 4,250 milliliters to liters and milliliters
Solution:
1 Divide: 4,250 ÷ 1,000 = 4 remainder 250
2 Write: 4 liters 250 milliliters
Total Small Units = (Large Units × Conversion) + Small Units
Mixed Units = Total ÷ Conversion (quotient = large, remainder = small)
7. Add and Subtract Mixed Metric Units
1 Line up units vertically (large with large, small with small)
2 Add or subtract the smaller units first
3 Add or subtract the larger units
4 Regroup if necessary (when small unit ≥ conversion factor)
Adding Mixed Metric Units:
Example 1: Add: 4 meters 65 centimeters + 2 meters 48 centimeters
Solution:
4 m 65 cm
+ 2 m 48 cm
————————————
6 m 113 cm
3 Regroup: 113 cm = 1 m 13 cm
4 Final: 6 m + 1 m 13 cm = 7 meters 13 centimeters
Example 2: Add: 3 kilograms 750 grams + 2 kilograms 400 grams
Solution:
1 Add grams: 750 + 400 = 1,150 grams
2 Add kilograms: 3 + 2 = 5 kilograms
3 Regroup: 1,150 grams = 1 kg 150 g
4 Final: 5 kg + 1 kg 150 g = 6 kilograms 150 grams
Example 3: Add: 5 liters 600 milliliters + 3 liters 800 milliliters
Solution:
1 Add milliliters: 600 + 800 = 1,400 mL
2 Add liters: 5 + 3 = 8 liters
3 Regroup: 1,400 mL = 1 L 400 mL
4 Final: 9 liters 400 milliliters
Subtracting Mixed Metric Units:
Example 4: Subtract: 8 meters 25 centimeters − 3 meters 40 centimeters
Solution:
1 Can't subtract 40 from 25, so regroup:
8 m 25 cm = 7 m 125 cm
2 Subtract centimeters: 125 − 40 = 85 cm
3 Subtract meters: 7 − 3 = 4 m
Answer: 4 meters 85 centimeters
Example 5: Subtract: 6 kilograms 200 grams − 2 kilograms 550 grams
Solution:
1 Can't subtract 550 from 200, so regroup:
6 kg 200 g = 5 kg 1,200 g
2 Subtract grams: 1,200 − 550 = 650 g
3 Subtract kilograms: 5 − 2 = 3 kg
Answer: 3 kilograms 650 grams
- Always line up units vertically for organization
- Regroup when smaller unit ≥ 100 (for cm/mL) or ≥ 1,000 (for g/mm)
- For subtraction, borrow 100 or 1,000 from the larger unit
- Check your work by converting everything to small units
- Metric regrouping is easier because of base 10!
8. Multi-Step Problems with Metric Unit Conversions
1 Read carefully and identify all measurements
2 Determine what conversions are needed
3 Convert all measurements to the same unit
4 Solve step by step
5 Check if your answer makes sense
Example 1 - Length:
A rope is 8 meters long. Three pieces are cut: 120 cm, 150 cm, and 2 m 30 cm. How much rope is left in meters?
Solution:
1 Convert all to centimeters:
Original: 8 m = 800 cm
Piece 1: 120 cm
Piece 2: 150 cm
Piece 3: 2 m 30 cm = 230 cm
2 Add pieces cut: 120 + 150 + 230 = 500 cm
3 Subtract from original: 800 − 500 = 300 cm
4 Convert to meters: 300 ÷ 100 = 3 meters
Example 2 - Mass:
A store has 5 kilograms of flour. They sell 800 grams, then 1 kg 200 g. How much flour remains in grams?
Solution:
1 Convert to grams: 5 kg = 5,000 g
2 First sale: 800 g
3 Second sale: 1 kg 200 g = 1,200 g
4 Total sold: 800 + 1,200 = 2,000 g
5 Remaining: 5,000 − 2,000 = 3,000 grams
Example 3 - Volume:
A tank holds 50 liters of water. You add 3 liters 500 milliliters three times. How much water is in the tank in liters?
Solution:
1 Convert addition to milliliters: 3 L 500 mL = 3,500 mL
2 Three times: 3,500 × 3 = 10,500 mL
3 Convert to liters: 10,500 ÷ 1,000 = 10.5 L
4 Add to original: 50 + 10.5 = 60.5 liters
Example 4 - Combined Operations:
Sara runs 2 kilometers 500 meters on Monday, 3,200 meters on Tuesday, and 1 km 800 m on Wednesday. What is her total distance in kilometers?
Solution:
1 Convert Monday: 2 km 500 m = 2,500 m
2 Tuesday: 3,200 m
3 Convert Wednesday: 1 km 800 m = 1,800 m
4 Total: 2,500 + 3,200 + 1,800 = 7,500 m
5 Convert to km: 7,500 ÷ 1,000 = 7.5 kilometers
- Convert everything to the smallest unit first to avoid decimals
- Write down each step clearly
- Use the ladder method for quick conversions
- Convert back to the requested unit at the end
- Draw diagrams or make lists to organize information
- Double-check your conversions!
9. Multi-Step Problems with Customary OR Metric Unit Conversions
1 Identify if the problem uses customary OR metric units
2 Use the correct conversion factors for that system
3 NEVER mix customary and metric in the same problem
4 Follow the appropriate conversion rules
Identifying the System:
| Customary Units | Metric Units |
|---|---|
| inches, feet, yards, miles | millimeters, centimeters, meters, kilometers |
| ounces, pounds, tons | milligrams, grams, kilograms |
| cups, pints, quarts, gallons | milliliters, liters |
Example 1 - CUSTOMARY System:
A recipe needs 3 cups of milk. You have 1 quart. Do you have enough? How much extra do you have in cups?
Solution:
1 Identify: Customary (cups, quarts)
2 Convert: 1 quart = 4 cups
3 Compare: Have 4 cups, need 3 cups
4 Yes, enough! Extra: 4 − 3 = 1 cup extra
Example 2 - METRIC System:
A bottle holds 2 liters. You drink 250 milliliters four times. How much is left in milliliters?
Solution:
1 Identify: Metric (liters, milliliters)
2 Convert original: 2 L = 2,000 mL
3 Total drunk: 250 × 4 = 1,000 mL
4 Remaining: 2,000 − 1,000 = 1,000 milliliters
Example 3 - CUSTOMARY System:
A board is 8 feet long. You cut off three pieces: 15 inches, 2 feet, and 18 inches. How much is left in inches?
Solution:
1 Identify: Customary (feet, inches)
2 Convert original: 8 feet = 96 inches
3 Piece 1: 15 inches
4 Piece 2: 2 feet = 24 inches
5 Piece 3: 18 inches
6 Total cut: 15 + 24 + 18 = 57 inches
7 Remaining: 96 − 57 = 39 inches
Example 4 - METRIC System:
Three packages weigh 2 kg 400 g, 1,800 grams, and 3 kg 200 g. What is the total weight in kilograms?
Solution:
1 Identify: Metric (kilograms, grams)
2 Convert package 1: 2 kg 400 g = 2,400 g
3 Package 2: 1,800 g
4 Convert package 3: 3 kg 200 g = 3,200 g
5 Total: 2,400 + 1,800 + 3,200 = 7,400 g
6 Convert to kg: 7,400 ÷ 1,000 = 7.4 kilograms
- First step: Identify which system the problem uses
- Use conversion factors specific to that system
- Metric: Base 10 (×/÷ by 10, 100, 1000)
- Customary: Various factors (12, 16, 2, 4, etc.)
- Never mix customary and metric in calculations
- Make a conversion chart for reference
📚 Master Metric Conversion Chart - Quick Reference
| LENGTH CONVERSIONS (Meter = Base) | ||
|---|---|---|
| 1 kilometer | = | 1,000 meters |
| 1 meter | = | 100 centimeters = 1,000 millimeters |
| 1 centimeter | = | 10 millimeters |
| MASS CONVERSIONS (Gram = Base) | ||
|---|---|---|
| 1 kilogram | = | 1,000 grams |
| 1 gram | = | 1,000 milligrams |
| 1 metric ton | = | 1,000 kilograms = 1,000,000 grams |
| VOLUME CONVERSIONS (Liter = Base) | ||
|---|---|---|
| 1 kiloliter | = | 1,000 liters |
| 1 liter | = | 1,000 milliliters |
| 1 milliliter | = | 1 cubic centimeter (cm³) |
🪜 METRIC LADDER REMINDER
King Henry Died By Drinking Chocolate Milk
Kilo → Hecto → Deka → Base Unit → Deci → Centi → Milli
Each step = ×10 or ÷10 | Move decimal point one place per step!
🎯 THE METRIC ADVANTAGE! 🎯
LARGER → SMALLER = MULTIPLY (× 10, 100, 1000)
SMALLER → LARGER = DIVIDE (÷ 10, 100, 1000)
🌟 The metric system is based on 10 - making it easier to convert! 🌟