We made a simple estimate of the mass of an E. coll cell by...

We made a simple estimate of the mass of an $E$. coll cell by assuming that such cells have the same density of water. However, a more reasonable estimate is that the density of the macromolecules of the cell is 1.3 times that of water $(\mathrm{BNID} 101502,104272) .$ As a result, the estimate of the mass of an $E$ coli cell is off by a bit. Using that two-thirds of the mass is water and that the remaining one-third is macromolecular, compute the percentage error made by treating the macromolecular density as the same as that of water.

Key Concepts

Percentage Error

Percentage error is a measure of the relative difference between an estimated or approximate value and an exact or theoretical value, expressed as a percentage. It provides a standardized way to evaluate the accuracy of an estimation method or assumption by comparing the magnitude of the error to the true value.

Mass Estimation from Density

Estimating mass from density involves multiplying the density of a substance by its volume. In mixed-material systems, using the correct density for each component is key to ensuring that the mass estimates are accurate, illustrating the importance of proper density values in scientific calculations.

Density

Density is a measure of the mass of a substance per unit volume. It is a fundamental property that helps determine how much matter is present in a specific volume and is essential in calculations related to mass, buoyancy, and material properties.

Composite or Weighted Average Density

When an object is composed of multiple substances with different densities, its overall density is determined as a weighted average based on the mass or volume fractions of each component. This concept ensures that contributions from each material are appropriately factored in to obtain an accurate effective density.

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