Before you write a density answer, compare it with known materials. Water is about 1000 kg/m³, common metals run from about 2700 to 19 300 kg/m³, and gases are around 1 kg/m³. If your answer is far outside the range for that kind of material, look for the slip.
This is the last lesson in mass, weight and density, and it joins the earlier skills into one habit of checking.
What is a reasonable density?
These are rounded reference values for sense-checking. For calculations, always use the values the question supplies.
| Material | Approx. density (kg/m³) | Approx. density (g/cm³) |
|---|---|---|
| Air | 1.2 | 0.0012 |
| Cooking oil | 920 | 0.92 |
| Water | 1000 | 1.0 |
| Aluminium | 2700 | 2.7 |
| Steel / iron | 7800 | 7.8 |
| Lead | 11 300 | 11.3 |
| Gold | 19 300 | 19.3 |
How do you test an answer?
- Place it on the table. Is it near a real material of the right kind?
- Ask which unit it is in. An answer of 8 kg/m³ for a metal is probably 8 g/cm³ with the wrong unit.
- Check the formula direction. ρ = m/V. If your answer is the reciprocal of a sensible value, you divided the wrong way round.
- Check the float test. A solid that sinks in water must be above 1000 kg/m³.
Worked example
A student measures 0.46 kg of cooking oil filling a 500 cm³ container and writes the density as 0.92 kg/m³. Decide whether this is reasonable, and correct it. (Invented data.)
Step 1, compare: 0.92 kg/m³ is close to the density of a gas, but oil is a liquid near 900 kg/m³. The answer is unreasonable.
Step 2, locate the slip: the student divided 0.46 kg by 0.5, treating 500 cm³ as 0.5 m³.
Step 3, correct the volume: 500 cm³ = 500 × 10⁻⁶ m³ = 5.0 × 10⁻⁴ m³.
Step 4, recalculate: ρ = 0.46 ÷ (5.0 × 10⁻⁴) = 920 kg/m³.
Check: 460 g ÷ 500 cm³ = 0.92 g/cm³ = 920 kg/m³. This is less than water, so the oil floats, as oil does.
The mistake to watch for
Mistaken answer: a 150 g rock with volume 60 cm³ has density 0.4 g/cm³.
The student divided 60 by 150, inverting the formula.
A rock with density 0.4 g/cm³ would float on water, which a rock does not. The correct value is 150 ÷ 60 = 2.5 g/cm³.
Also quote a sensible number of significant figures. The bounds and rounding explainer shows what a rounded value means.
Check yourself
1. A solid steel bar is reported to have density 8 kg/m³. What has probably gone wrong?
Show answer
Steel is about 7800 kg/m³ (7.8 g/cm³). The value 8 is most likely in g/cm³ but written with the wrong unit, or a conversion by 1000 was skipped.
2. A student finds a liquid with density 1.3 g/cm³ and says “it floats on water”. Is this reasonable?
Show answer
Not reasonable. 1.3 g/cm³ is greater than water’s 1.0 g/cm³, so the liquid would sink in water. The statement contradicts the number.
3. A 240 g metal block has volume 30 cm³ and a student writes ρ = 0.125 g/cm³. Decide and correct.
Show answer
0.125 is 30 ÷ 240, so the formula was inverted and the answer is unreasonable for a metal. Correct: 240 ÷ 30 = 8.0 g/cm³ (8000 kg/m³), which is close to steel.
Where this leads next
Put everything together in the mass, weight and density practice set. Return to the topic overview to see how the five lessons connect.
Sense-checking is a habit that a teacher can coach directly while watching you work, as in online one-to-one Physics tuition.