Math Problem Statement

Convert a density of 0.987 g/mL to the SI unit for density, which is kg/m3.

Solution

To convert a density from grams per milliliter (g/mL) to kilograms per cubic meter (kg/m³), we follow these conversion steps:

  1. Convert grams to kilograms:
    1g=0.001kg1 \, \text{g} = 0.001 \, \text{kg}.

  2. Convert milliliters to cubic meters:
    1mL=1×106m31 \, \text{mL} = 1 \times 10^{-6} \, \text{m}^3.

Conversion calculation:

Given:
0.987g/mL0.987 \, \text{g/mL}.

Convert to kilograms per cubic meter (kg/m³):

0.987g/mL=0.987×0.001kg1g×1mL1×106m30.987 \, \text{g/mL} = 0.987 \times \frac{0.001 \, \text{kg}}{1 \, \text{g}} \times \frac{1 \, \text{mL}}{1 \times 10^{-6} \, \text{m}^3}

=0.987×1000kg/m3= 0.987 \times 1000 \, \text{kg/m}^3

=987kg/m3= 987 \, \text{kg/m}^3

Final Answer:

The density is 987kg/m3987 \, \text{kg/m}^3.

Would you like more details or have any questions?


Here are five related questions for practice:

  1. How would you convert 1.5 g/mL to kg/m³?
  2. What is the density of water in kg/m³ if it is 1 g/mL?
  3. Convert 1200 kg/m³ to g/mL.
  4. If a substance has a density of 0.8 g/mL, what is it in kg/m³?
  5. How would you convert 2.3 kg/L to kg/m³?

Tip: Always ensure consistency in units when converting—especially between different volume measures like milliliters and cubic meters.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Density
Metric System

Formulas

1 g/mL = 1000 kg/m³
Density (ρ) = mass/volume

Theorems

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Suitable Grade Level

Grades 9-12