CC.3 Convert and compare metric units of mass
What is mass?
Mass is the amount of matter in an object. It tells us how much "stuff" is in something. Mass is not the same as weight, but in everyday life, we often use the two words in similar ways. In the metric system, the base unit for mass is the gram (g). A small paper clip has a mass of about 1 gram.
- A single raisin has a mass of about 1 gram.
- A nickel coin has a mass of about 5 grams.
- A slice of bread has a mass of about 25 grams.
When you measure mass, you are finding out how heavy something is compared to a standard unit. The gram is the standard unit for small objects.
Metric units of mass
The metric system uses prefixes to show larger or smaller units. For mass, the three most common units are the gram (g), the kilogram (kg), and the milligram (mg). The prefix "kilo-" means 1,000, so a kilogram is 1,000 grams. The prefix "milli-" means one-thousandth, so a milligram is one-thousandth of a gram.
- 1 kilogram (kg) = 1,000 grams (g)
- 1 gram (g) = 1,000 milligrams (mg)
- 1 kilogram (kg) = 1,000,000 milligrams (mg)
The metric system is based on powers of 10. This makes converting between units simple: you multiply or divide by 10, 100, or 1,000.
Converting kilograms to grams
To convert from a larger unit to a smaller unit, you multiply. Since 1 kilogram equals 1,000 grams, you multiply the number of kilograms by 1,000 to find the number of grams.
- 2 kg = 2 × 1,000 = 2,000 g
- 5 kg = 5 × 1,000 = 5,000 g
- 0.5 kg = 0.5 × 1,000 = 500 g
- 3.25 kg = 3.25 × 1,000 = 3,250 g
When you multiply by 1,000, the decimal point moves three places to the right. For example, 3.25 kg becomes 3,250 g.
Converting grams to kilograms
To convert from a smaller unit to a larger unit, you divide. Since 1,000 grams equals 1 kilogram, you divide the number of grams by 1,000 to find the number of kilograms.
- 4,000 g = 4,000 ÷ 1,000 = 4 kg
- 7,500 g = 7,500 ÷ 1,000 = 7.5 kg
- 12,000 g = 12,000 ÷ 1,000 = 12 kg
- 250 g = 250 ÷ 1,000 = 0.25 kg
When you divide by 1,000, the decimal point moves three places to the left. For example, 7,500 g becomes 7.5 kg.
Converting grams to milligrams
To convert from grams to milligrams, you multiply by 1,000 because 1 gram equals 1,000 milligrams. This is useful when measuring very small masses, such as medicine dosages.
- 3 g = 3 × 1,000 = 3,000 mg
- 0.8 g = 0.8 × 1,000 = 800 mg
- 1.5 g = 1.5 × 1,000 = 1,500 mg
Milligrams are used for very light objects. A grain of salt has a mass of about 0.5 milligrams.
Converting milligrams to grams
To convert from milligrams to grams, you divide by 1,000 because 1,000 milligrams equal 1 gram. This conversion helps you express small masses in a larger unit.
- 5,000 mg = 5,000 ÷ 1,000 = 5 g
- 2,500 mg = 2,500 ÷ 1,000 = 2.5 g
- 750 mg = 750 ÷ 1,000 = 0.75 g
Remember: dividing by 1,000 moves the decimal point three places to the left.
Using a conversion table
A conversion table helps you see the relationship between units at a glance. You can use it to check your work or to convert between units quickly.
- 1 kilogram (kg) = 1,000 grams (g)
- 1 gram (g) = 1,000 milligrams (mg)
- 1 kilogram (kg) = 1,000,000 milligrams (mg)
- 1,000 kilograms (kg) = 1 metric ton (t)
The metric ton is used for very heavy objects, such as cars or large animals. A small car has a mass of about 1 metric ton.
Comparing metric units of mass
To compare two masses, they must be in the same unit. If they are not, convert one or both masses so that they share a unit. Then compare the numbers using the symbols > (greater than), < (less than), or = (equal to).
- Compare 2 kg and 1,500 g. Convert: 2 kg = 2,000 g. Since 2,000 > 1,500, we write 2 kg > 1,500 g.
- Compare 3,000 g and 3 kg. Convert: 3 kg = 3,000 g. Since 3,000 = 3,000, we write 3,000 g = 3 kg.
- Compare 500 mg and 0.5 g. Convert: 0.5 g = 500 mg. Since 500 = 500, we write 500 mg = 0.5 g.
- Compare 1.2 kg and 1,100 g. Convert: 1.2 kg = 1,200 g. Since 1,200 > 1,100, we write 1.2 kg > 1,100 g.
Always convert to the smaller unit to avoid working with decimals. For example, convert kilograms to grams before comparing.
Solving word problems with metric mass
Word problems often require you to convert units before you can add, subtract, multiply, or divide. Read the problem carefully, identify the units, and convert them to the same unit before calculating.
- A bag of flour has a mass of 2 kg. A bag of sugar has a mass of 1,500 g. What is the total mass in grams? Convert: 2 kg = 2,000 g. Add: 2,000 + 1,500 = 3,500 g.
- A package weighs 4,500 g. How many kilograms is that? Divide: 4,500 ÷ 1,000 = 4.5 kg.
- Maria's backpack has a mass of 3.2 kg. Her friend's backpack has a mass of 2,800 g. Whose backpack is heavier? Convert: 3.2 kg = 3,200 g. Compare: 3,200 > 2,800, so Maria's backpack is heavier.
When solving word problems, underline the numbers and circle the units. This helps you keep track of what needs to be converted.
Choosing the best unit of mass
Choosing the right unit makes your measurement clear and easy to understand. Use milligrams for very small objects, grams for small objects, kilograms for heavier objects, and metric tons for very heavy objects.
- A tablet of medicine: milligrams (mg)
- A pencil: grams (g)
- A bag of groceries: kilograms (kg)
- A small car: metric tons (t)
If you are unsure which unit to use, think about the size of the object compared to a paper clip (1 gram) or a large textbook (1 kilogram).
Estimating mass
Estimation helps you check if your answer is reasonable. Use familiar objects as benchmarks. For example, a paper clip is about 1 gram, and a liter of water is about 1 kilogram.
- A slice of bread is about 25 grams.
- A dictionary is about 1 kilogram.
- A bicycle is about 10 kilograms.
- A refrigerator is about 100 kilograms.
Estimation is a powerful tool. It helps you catch mistakes when converting or comparing units.
Common mistakes to avoid
Students often make mistakes when converting metric units. One common mistake is multiplying when they should divide, or dividing when they should multiply. Another mistake is moving the decimal point the wrong number of places.
- Incorrect: 5 kg = 5,000,000 g (multiplied by 1,000,000 instead of 1,000)
- Correct: 5 kg = 5,000 g
- Incorrect: 3,000 g = 300 kg (divided by 10 instead of 1,000)
- Correct: 3,000 g = 3 kg
Always double-check your conversion by asking: "Is the new number larger or smaller?" When converting to a smaller unit, the number should be larger. When converting to a larger unit, the number should be smaller.
Practice with real-world examples
Applying your skills to real-world situations makes the math meaningful. Try converting and comparing masses in cooking, science, and shopping.
- A recipe calls for 0.5 kg of butter. You have 400 g. Do you have enough? Convert: 0.5 kg = 500 g. Since 500 > 400, you do not have enough.
- A science experiment requires 2,500 mg of salt. You have 2.5 g. Do you have enough? Convert: 2.5 g = 2,500 mg. Yes, you have exactly enough.
- A suitcase weighs 23 kg. The airline limit is 20,000 g. Is the suitcase over the limit? Convert: 23 kg = 23,000 g. Since 23,000 > 20,000, yes, it is over the limit.
Real-world practice helps you see why converting and comparing metric units of mass is an important life skill.
Common Core alignment: CCSS.MATH.CONTENT.4.MD.A.1 – Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
Notes for teachers
This resource is designed to provide clear explanations, examples, and practice for learners of different needs and levels of support. It may be used for whole-class instruction, guided practice, independent learning, review, homework, or additional reinforcement at home.