Last reviewed: 7 November 2026
Updated November 2026. These Grade 9 mass, weight and density notes cover converting units of mass, the difference between mass and weight, and how to calculate density. The key formula is density = mass ÷ volume. A 200 g stone with a volume of 80 cm³ has a density of 200 ÷ 80 = 2.5 g/cm³. Rearranging the same formula gives mass = density × volume and volume = mass ÷ density.
All questions here are original practice for Kenyan junior school learners, not an official paper. For the full list of topics, see our Grade 9 maths revision guide and the Grade 9 notes hub. Volume of solids is covered in our volume and capacity notes, which you will need for density questions.
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What the Grade 9 Curriculum Expects
In the Grade 9 Mathematics design from the Kenya Institute of Curriculum Development, “Mass, Volume, Weight and Density” is a sub-strand under Measurements. Learners should convert units of mass, relate mass and weight, determine mass, volume and density of substances, and apply density in real life. The design is listed on the KICD Grade Nine curriculum designs page. These notes stay within that scope.
Converting Units of Mass
The kilogram is the SI base unit of mass, as set out in the NIST summary of SI units. The other everyday units are multiples or fractions of it.
| Unit | Equivalent |
|---|---|
| 1 tonne (t) | 1,000 kg |
| 1 kilogram (kg) | 1,000 g |
| 1 gram (g) | 1,000 mg |
To go from a bigger unit to a smaller one, multiply. To go from a smaller unit to a bigger one, divide. So 3.4 kg = 3.4 × 1,000 = 3,400 g, and 750 g = 750 ÷ 1,000 = 0.75 kg. A lorry carrying 12,500 kg of maize is carrying 12,500 ÷ 1,000 = 12.5 tonnes.
Worked example: shopping problem
A trader packs 2.4 kg of sugar into 300 g packets. How many packets? Convert to the same unit first: 2.4 kg = 2,400 g. Then 2,400 ÷ 300 = 8 packets. Most errors in this topic come from dividing before converting.
Mass and Weight Are Not the Same
- Mass is the amount of matter in an object. It is measured in kilograms and does not change from place to place.
- Weight is the pull of gravity on that mass. It is a force, measured in newtons (N), and it changes if gravity changes, for example on the Moon.
Weight = mass × gravitational field strength. Near the Earth’s surface the field strength is about 9.8 N/kg, and many school questions round it to 10 N/kg. Always use the value the question gives. With 10 N/kg, a 50 kg learner weighs 50 × 10 = 500 N. In everyday speech people say “I weigh 50 kg”, but in maths and science that number is a mass.
How to Calculate Density
Density tells you how much mass is packed into each unit of volume.
| Find | Formula |
|---|---|
| Density | mass ÷ volume |
| Mass | density × volume |
| Volume | mass ÷ density |
Common units are g/cm³ and kg/m³. Because 1 m³ = 1,000,000 cm³ and 1 kg = 1,000 g, a density of 1 g/cm³ equals 1,000 kg/m³. To convert from g/cm³ to kg/m³, multiply by 1,000. Pure water has a density of about 1 g/cm³ at room temperature, which is why it is a useful comparison.
Worked example: a regular solid
A wooden block measures 10 cm by 5 cm by 4 cm and has a mass of 140 g. Find its density.
- Volume = 10 × 5 × 4 = 200 cm³.
- Density = 140 ÷ 200 = 0.7 g/cm³.
- In kg/m³: 0.7 × 1,000 = 700 kg/m³.
Its density is less than that of water, which is consistent with most dry wood floating.
Worked example: an irregular object
A measuring cylinder holds 60 cm³ of water. A small stone is lowered in and the level rises to 85 cm³. The stone has a mass of 65 g. Volume of stone = 85 − 60 = 25 cm³. Density = 65 ÷ 25 = 2.6 g/cm³. This “displacement” method is the practical activity the curriculum suggests for objects without a regular shape.
Worked example: finding mass
Cooking oil in this example has a density of 0.92 g/cm³. What is the mass of 500 cm³ of it? Mass = 0.92 × 500 = 460 g. A 500 ml bottle of oil therefore has less mass than 500 ml of water, about 500 g.
Original Practice Questions With Worked Answers
- Convert 0.35 tonnes to kilograms. 0.35 × 1,000 = 350 kg.
- A box has a mass of 8 kg. Find its weight using g = 10 N/kg. 8 × 10 = 80 N.
- A metal cube of side 3 cm has a mass of 243 g. Find its density. Volume = 3 × 3 × 3 = 27 cm³. Density = 243 ÷ 27 = 9 g/cm³.
- Convert 2.5 g/cm³ to kg/m³. 2.5 × 1,000 = 2,500 kg/m³.
- A liquid has density 1.2 g/cm³. What volume has a mass of 600 g? Volume = 600 ÷ 1.2 = 500 cm³.
- Does an astronaut’s mass change on the Moon? No. The mass stays the same; only the weight becomes smaller because gravity is weaker.
Cover the answers and work each question first. Then try timed questions in the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the formula for density in Grade 9 maths?
Density = mass ÷ volume. If you know any two of mass, volume and density, you can find the third by rearranging the formula.
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms. Weight is the force of gravity on that mass, measured in newtons, and it changes when gravity changes.
How do I convert g/cm³ to kg/m³?
Multiply by 1,000. For example, 0.8 g/cm³ = 800 kg/m³.
How do I find the volume of an irregular object?
Lower it into a measuring cylinder of water and record the rise in water level. The rise in volume equals the volume of the object, as long as it sinks fully and does not absorb water.