Question

What is the density of water in kgdm^–3 if its density in gcm^–3 is 0.863?

• A. 7.86
• B. 0.863
• C. 8.63
• D. 4.6

Answer 1

The Correct Option is B

Concept:
When converting units of density, it's important to understand the relationship between different metric volume and mass units. In this case, we are asked to convert the density of water from grams per cubic centimeter (g/cm³) to kilograms per cubic decimeter (kg/dm³).

Let’s break it down:
• 1 gram (g) = 0.001 kilogram (kg)
• 1 cubic centimeter (cm³) = 0.001 cubic decimeter (dm³)

So, when we convert both the numerator (mass) and the denominator (volume), the factors cancel out:
1 g/cm³ = \(\frac{0.001 \text{ kg}}{0.001 \text{ dm}^3} = 1 \text{ kg/dm}^3\)

Step-by-step:
• Given density = 0.863 g/cm³
• Using the equivalence above, this directly converts to:
→ 0.863 kg/dm³

Conclusion:
Since 1 g/cm³ = 1 kg/dm³, the density of water remains numerically the same when converted between these units.
Thus, the correct answer is (B) 0.863.