Metric Conversions. Grade 8 Mathematics: Metric Conversions - Length, Mass, and Capacity Subtopics Navigator Introduction to Metric System Converting Length Units Converting Mass Units Converting Capacity Units Conversion Strategies Real-World Applications Cumulative Exercises Conclusion Lesson Objectives Understand the metric system and its base units Convert between different metric units of length (km, m, cm, mm) Convert between different metric units of mass (kg, g, mg) Convert between different metric units of capacity (L, mL) Apply conversion strategies to solve real-world problems Metric System The metric system is an international decimal system of measurement used by most countries worldwide. It's based on powers of ten, which makes conversions between units straightforward. The three main metric units we'll focus on are: Length: meter (m) is the base unit Mass: gram (g) is the base unit Capacity: liter (L) is the base unit Kilo (k) Thousand 1000 units → Hecto (h) Hundred 100 units → Deca (da) Ten 10 units → Base m/g/l 1 unit → Deci (d) Tenth 0.1 units → Centi (c) Hundredth 0.01 units → Milli (m) Thousandth 0.001 units Metric Prefixes: Kilo- means 1000 (e.g., 1 kilometer = 1000 meters) Centi- means 1/100 (e.g., 1 centimeter = 0.01 meters) Milli- means 1/1000 (e.g., 1 milliliter = 0.001 liters) Understanding Metric Units How many meters are in a kilometer? What fraction of a meter is a centimeter? If you have 1000 milliliters, how many liters do you have? Converting Length Units Length measurements in the metric system use the meter as the base unit. Common units include kilometers (km), meters (m), centimeters (cm), and millimeters (mm). Unit Relationship to Meter Example Conversion Kilometer (km) 1 km = 1000 m 2.5 km = 2500 m Meter (m) Base unit 1 m = 1 m Centimeter (cm) 1 m = 100 cm 150 cm = 1.5 m Millimeter (mm) 1 m = 1000 mm 500 mm = 0.5 m Example 1: Converting Larger to Smaller Units Convert 3.2 meters to centimeters. Since 1 m = 100 cm, we multiply: 3.2 × 100 = 320 cm Answer: 320 cm Example 2: Converting Smaller to Larger Units Convert 850 millimeters to meters. Since 1 m = 1000 mm, we divide: 850 ÷ 1000 = 0.85 m Answer: 0.85 m Example 3: Multi-step Conversion Convert 2.4 km to cm. First, convert km to m: 2.4 × 1000 = 2400 m Then, convert m to cm: 2400 × 100 = 240,000 cm Answer: 240,000 cm Exercises (Length Conversions) Convert 5.7 km to meters Convert 245 cm to meters Convert 8.3 m to millimeters Convert 1250 mm to centimeters Convert 0.75 km to centimeters Converting Mass Units Mass measurements in the metric system use the gram as the base unit. Common units include kilograms (kg), grams (g), and milligrams (mg). Unit Relationship to Gram Example Conversion Kilogram (kg) 1 kg = 1000 g 2.3 kg = 2300 g Gram (g) Base unit 1 g = 1 g Milligram (mg) 1 g = 1000 mg 500 mg = 0.5 g Example 4: Converting Kilograms to Grams Convert 4.25 kg to grams. Since 1 kg = 1000 g, we multiply: 4.25 × 1000 = 4250 g Answer: 4250 g Example 5: Converting Milligrams to Grams Convert 750 mg to grams. Since 1 g = 1000 mg, we divide: 750 ÷ 1000 = 0.75 g Answer: 0.75 g Example 6: Multi-step Mass Conversion Convert 0.035 kg to mg. First, convert kg to g: 0.035 × 1000 = 35 g Then, convert g to mg: 35 × 1000 = 35,000 mg Answer: 35,000 mg Exercises (Mass Conversions) Convert 3.8 kg to grams Convert 1250 g to kilograms Convert 0.45 g to milligrams Convert 25,000 mg to grams Convert 1.2 kg to milligrams Converting Capacity Units Capacity (volume of liquids) measurements in the metric system use the liter as the base unit. Common units include liters (L) and milliliters (mL). Unit Relationship to Liter Example Conversion Liter (L) Base unit 1 L = 1 L Milliliter (mL) 1 L = 1000 mL 350 mL = 0.35 L Centiliter (cL) 1 L = 100 cL 75 cL = 0.75 L Example 7: Converting Liters to Milliliters Convert 2.75 L to milliliters. Since 1 L = 1000 mL, we multiply: 2.75 × 1000 = 2750 mL Answer: 2750 mL Example 8: Converting Milliliters to Liters Convert 480 mL to liters. Since 1 L = 1000 mL, we divide: 480 ÷ 1000 = 0.48 L Answer: 0.48 L Example 9: Working with Centiliters Convert 125 cL to liters. Since 1 L = 100 cL, we divide: 125 ÷ 100 = 1.25 L Answer: 1.25 L Exercises (Capacity Conversions) Convert 4.2 L to milliliters Convert 850 mL to liters Convert 0.3 L to centiliters Convert 250 cL to liters Convert 1500 mL to centiliters Conversion Strategies When converting between metric units, remember these key strategies: Conversion Type Operation Reason Larger unit to smaller unit Multiply You need more of the smaller units Smaller unit to larger unit Divide You need fewer of the larger units Using the metric ladder Move decimal point Each step is a power of 10 Using the Decimal Point Method Convert 3.5 km to m: From km to m is 3 steps down on the metric ladder (k→h→da→m) Move decimal point 3 places to the right: 3.5 km = 3500 m Convert 250 mm to m: From mm to m is 3 steps up on the metric ladder (mm→cm→dm→m) Move decimal point 3 places to the left: 250 mm = 0.250 m Conversion Strategies Practice When converting from cm to m, do you multiply or divide? How many places do you move the decimal when converting from kg to g? What direction do you move the decimal when converting from mL to L? Real-World Applications Metric conversions are used in many everyday situations: Cooking - Converting between mL and L for recipes Travel - Converting km to m for distance measurements Shopping - Comparing prices per kg or per g Medicine - Measuring dosages in mg or mL Sports - Measuring track distances in m or km Example 10: Cooking Application A recipe calls for 1.5 L of milk, but you only have a 250 mL measuring cup. How many cups do you need? First, convert 1.5 L to mL: 1.5 × 1000 = 1500 mL Then divide by cup size: 1500 ÷ 250 = 6 cups Answer: 6 cups Example 11: Travel Application The distance from your home to school is 2.8 km. How many meters is this? Convert km to m: 2.8 × 1000 = 2800 m Answer: 2800 m Example 12: Shopping Application A 500 g package of cheese costs $6.50. What is the price per kilogram? First, find how many 500 g units in 1 kg: 1000 ÷ 500 = 2 Then multiply: $6.50 × 2 = $13.00 per kg Answer: $13.00 per kg Real-World Problems A water bottle holds 750 mL. How many liters is this? A person's height is 165 cm. How many meters is this? A pill contains 250 mg of medicine. How many grams is this? A car travels 15 km to work each day. How many meters is this? A recipe requires 300 mL of oil. How many 0.5 L bottles do you need to buy? Cumulative Exercises Convert 4.5 km to meters Convert 3250 g to kilograms Convert 0.8 L to milliliters Convert 150 cm to meters Convert 25,000 mg to grams Convert 850 mL to liters Convert 3.2 m to centimeters Convert 0.045 kg to milligrams Convert 125 cL to liters Convert 5,600 mm to meters A swimming pool is 25 m long. How many centimeters is this? A medicine dosage is 0.5 g. How many milligrams is this? A juice box contains 200 mL. How many liters would 5 juice boxes contain? A person weighs 68 kg. How many grams is this? A road sign says the next town is 12 km away. How many meters is this? Show/Hide Answers Problem: Convert 4.5 km to meters Step 1: 1 km = 1000 m Step 2: 4.5 × 1000 = 4500 m Answer: 4500 m Problem: Convert 3250 g to kilograms Step 1: 1 kg = 1000 g Step 2: 3250 ÷ 1000 = 3.25 kg Answer: 3.25 kg Problem: Convert 0.8 L to milliliters Step 1: 1 L = 1000 mL Step 2: 0.8 × 1000 = 800 mL Answer: 800 mL Problem: Convert 150 cm to meters Step 1: 1 m = 100 cm Step 2: 150 ÷ 100 = 1.5 m Answer: 1.5 m Problem: Convert 25,000 mg to grams Step 1: 1 g = 1000 mg Step 2: 25,000 ÷ 1000 = 25 g Answer: 25 g Problem: Convert 850 mL to liters Step 1: 1 L = 1000 mL Step 2: 850 ÷ 1000 = 0.85 L Answer: 0.85 L Problem: Convert 3.2 m to centimeters Step 1: 1 m = 100 cm Step 2: 3.2 × 100 = 320 cm Answer: 320 cm Problem: Convert 0.045 kg to milligrams Step 1: First convert kg to g: 0.045 × 1000 = 45 g Step 2: Then convert g to mg: 45 × 1000 = 45,000 mg Answer: 45,000 mg Problem: Convert 125 cL to liters Step 1: 1 L = 100 cL Step 2: 125 ÷ 100 = 1.25 L Answer: 1.25 L Problem: Convert 5,600 mm to meters Step 1: 1 m = 1000 mm Step 2: 5,600 ÷ 1000 = 5.6 m Answer: 5.6 m Problem: A swimming pool is 25 m long. How many centimeters is this? Step 1: 1 m = 100 cm Step 2: 25 × 100 = 2500 cm Answer: 2500 cm Problem: A medicine dosage is 0.5 g. How many milligrams is this? Step 1: 1 g = 1000 mg Step 2: 0.5 × 1000 = 500 mg Answer: 500 mg Problem: A juice box contains 200 mL. How many liters would 5 juice boxes contain? Step 1: Total mL: 200 × 5 = 1000 mL Step 2: Convert to liters: 1000 ÷ 1000 = 1 L Answer: 1 L Problem: A person weighs 68 kg. How many grams is this? Step 1: 1 kg = 1000 g Step 2: 68 × 1000 = 68,000 g Answer: 68,000 g Problem: A road sign says the next town is 12 km away. How many meters is this? Step 1: 1 km = 1000 m Step 2: 12 × 1000 = 12,000 m Answer: 12,000 m Conclusion/Recap In this lesson, we've explored metric conversions for length, mass, and capacity. We learned that the metric system is based on powers of ten, which makes conversions straightforward. Remember these key points: To convert from larger to smaller units, multiply To convert from smaller to larger units, divide You can use the metric ladder to move the decimal point Common conversions: 1 km = 1000 m, 1 kg = 1000 g, 1 L = 1000 mL Metric conversions are essential skills used in everyday life, from cooking and shopping to travel and medicine. With practice, these conversions will become second nature. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c
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