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Density worksheet

Grades 6–7 · CCSS 6.RP.A.3.d

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Density: 2
- From: Pounds per US gallon (lb/US gal)
- To: Kilograms per cubic meter (kg/m³)
Find: In kilograms per cubic meter
Answer
2.
Problem 2.
- Density: 2
- From: Pounds per cubic inch (lb/in³)
- To: Pounds per imperial gallon (lb/imp gal)
Find: In pounds per imperial gallon
Answer
3.
Problem 3.
- Density: 1
- From: Grams per milliliter (g/mL)
- To: Milligrams per milliliter (mg/mL)
Find: In milligrams per milliliter
Answer
4.
Problem 4.
- Density: 1
- From: Milligrams per milliliter (mg/mL)
- To: Ounces per cubic inch (oz/in³)
Find: In ounces per cubic inch
Answer
5.
Problem 5.
- Density: 1
- From: Pounds per cubic inch (lb/in³)
- To: Ounces per cubic inch (oz/in³)
Find: In ounces per cubic inch
Answer
6.
Problem 6.
- Density: 2
- From: Ounces per cubic inch (oz/in³)
- To: Kilograms per liter (kg/L)
Find: In kilograms per liter
Answer
7.
Problem 7.
- Density: 1
- From: Kilograms per liter (kg/L)
- To: Ounces per cubic inch (oz/in³)
Find: In ounces per cubic inch
Answer
8.
Problem 8.
- Density: 1
- From: Grams per milliliter (g/mL)
- To: Pounds per imperial gallon (lb/imp gal)
Find: In pounds per imperial gallon
Answer
9.
Problem 9.
- Density: 2
- From: Pounds per cubic inch (lb/in³)
- To: Ounces per US gallon (oz/US gal)
Find: In ounces per us gallon
Answer
10.
Problem 10.
- Density: 2
- From: Metric tonnes per cubic meter (t/m³)
- To: Pounds per US gallon (lb/US gal)
Find: In pounds per us gallon
Answer

Answer key: Density worksheet

1. In kilograms per cubic meter: 239.65 kg/m³
1. Convert to kilograms per cubic meter: 1 lb/US gal = 119.8264273169 kg/m³, so multiply
  $2 lb/US gal \times 119.8264273169$ $= 239.6528546338 kg/m³$
2. In pounds per imperial gallon: 554.84 lb/imp gal
1. Convert to kilograms per cubic meter: 1 lb/in³ = 27,679.9047102031 kg/m³, so multiply
  $2 lb/in³ \times 27,679.9047102031$ $= 55,359.8094204063 kg/m³$
2. Convert to pounds per imperial gallon: 1 lb/imp gal = 99.7763726631 kg/m³, so divide
  $\frac{55,359.8094204063 kg/m³}{99.7763726631}$ $= 554.8388655832 lb/imp gal$
3. In milligrams per milliliter: 1,000 mg/mL
1. Convert to kilograms per cubic meter: 1 g/mL = 1,000 kg/m³, so multiply
  $1 g/mL \times 1,000$ $= 1,000 kg/m³$
4. In ounces per cubic inch: 5.78e-4 oz/in³
1. Convert to ounces per cubic inch: 1 oz/in³ = 1,729.9940443877 kg/m³, so divide
  $\frac{1 kg/m³}{1,729.9940443877}$ $= 0.0005780367 oz/in³$
5. In ounces per cubic inch: 16 oz/in³
1. Convert to kilograms per cubic meter: 1 lb/in³ = 27,679.9047102031 kg/m³, so multiply
  $1 lb/in³ \times 27,679.9047102031$ $= 27,679.9047102031 kg/m³$
2. Convert to ounces per cubic inch: 1 oz/in³ = 1,729.9940443877 kg/m³, so divide
  $\frac{27,679.9047102031 kg/m³}{1,729.9940443877}$ $= 16 oz/in³$
6. In kilograms per liter: 3.46 kg/L
1. Convert to kilograms per cubic meter: 1 oz/in³ = 1,729.9940443877 kg/m³, so multiply
  $2 oz/in³ \times 1,729.9940443877$ $= 3,459.9880887754 kg/m³$
2. Convert to kilograms per liter: 1 kg/L = 1,000 kg/m³, so divide
  $\frac{3,459.9880887754 kg/m³}{1,000}$ $= 3.4599880888 kg/L$
7. In ounces per cubic inch: 0.58 oz/in³
1. Convert to kilograms per cubic meter: 1 kg/L = 1,000 kg/m³, so multiply
  $1 kg/L \times 1,000$ $= 1,000 kg/m³$
2. Convert to ounces per cubic inch: 1 oz/in³ = 1,729.9940443877 kg/m³, so divide
  $\frac{1,000 kg/m³}{1,729.9940443877}$ $= 0.578036672 oz/in³$
8. In pounds per imperial gallon: 10.02 lb/imp gal
1. Convert to kilograms per cubic meter: 1 g/mL = 1,000 kg/m³, so multiply
  $1 g/mL \times 1,000$ $= 1,000 kg/m³$
2. Convert to pounds per imperial gallon: 1 lb/imp gal = 99.7763726631 kg/m³, so divide
  $\frac{1,000 kg/m³}{99.7763726631}$ $= 10.022412855 lb/imp gal$
9. In ounces per us gallon: 7,392 oz/US gal
1. Convert to kilograms per cubic meter: 1 lb/in³ = 27,679.9047102031 kg/m³, so multiply
  $2 lb/in³ \times 27,679.9047102031$ $= 55,359.8094204063 kg/m³$
2. Convert to ounces per us gallon: 1 oz/US gal = 7.4891517073 kg/m³, so divide
  $\frac{55,359.8094204063 kg/m³}{7.4891517073}$ $= 7,392 oz/US gal$
10. In pounds per us gallon: 16.69 lb/US gal
1. Convert to kilograms per cubic meter: 1 t/m³ = 1,000 kg/m³, so multiply
  $2 t/m³ \times 1,000$ $= 2,000 kg/m³$
2. Convert to pounds per us gallon: 1 lb/US gal = 119.8264273169 kg/m³, so divide
  $\frac{2,000 kg/m³}{119.8264273169}$ $= 16.690808904 lb/US gal$