Question

A red blood cell measures about \(7.8 \times 10^{-6} \mathrm{~m}\) in diameter. What is its diameter in nanometers?

Short answer

The diameter of the red blood cell is \(7.8 \times 10^{3}\) nanometers.

Step-by-step solution

Understanding the Conversion

1 nanometer (nm) is equal to 1 x 10^(-9) meters. To convert meters to nanometers, you multiply the number of meters by 10^9.

Setting Up the Conversion

Multiply the diameter of the red blood cell in meters by 10^9 to convert it to nanometers.

Performing the Conversion

The diameter in meters is \(7.8 \times 10^{-6}\). Multiplying by 10^9 gives: \(7.8 \times 10^{-6} \times 10^{9} = 7.8 \times 10^{3}\) nanometers.

Key concepts

Metric Unit Conversion

Metric unit conversion is a fundamental concept in science and mathematics, as it allows us to express measurements in different units of scale. For instance, converting meters to nanometers involves understanding the relationship between these units. One meter is equivalent to 1,000,000,000 nanometers (\(1 \text{ m} = 1 \times 10^{9} \text{ nm}\)). When converting from a larger unit to a smaller unit, you multiply by a factor of 10 for each step down in scale.

To effectively convert a measurement like the diameter of a red blood cell from meters to nanometers, you would multiply the value in meters by \(10^{9}\), because nanometers are much smaller and more numerous within a meter. This multiplication will shift the decimal point nine places to the right, giving us the diameter in nanometers.

• Example: Converting 0.0000078 meters to nanometers involves multiplying by \(10^{9}\), which equals 7,800 nanometers.

Scientific Notation

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used in sciences like physics, chemistry, and biology where large ranges of magnitudes are encountered. In scientific notation, numbers are written as the product of two parts: a coefficient and \(10 \text{ raised to a power}\).

The coefficient must be a number greater than or equal to 1 and less than 10, and the exponent is an integer that represents how many places the decimal point would be moved to convert the number into a coefficient between 1 and 10.

• For example, the diameter of a red blood cell (\(7.8 \times 10^{-6} \text{ m}\)) is written so that it clearly indicates a number much smaller than one meter.

Using scientific notation simplifies computations like unit conversions, as it's clear to see how powers of ten will manipulate the value.

Nanotechnology in Biology

Nanotechnology in biology, often referred to as 'nanobiology', is a subfield of nanoscience that uses nanoscale tools and processes to study and manipulate biological systems. This is crucial since many biological processes occur at the nanometer scale. For instance, a red blood cell's diameter is approximately 7,800 nanometers, and understanding this scale helps in designing targeted drug delivery systems that interact at the cellular level.

With the advancements in nanotechnology, scientists are now capable of engineering materials and devices that operate within the same size regime as proteins and DNA, allowing for innovation in areas such as gene therapy, diagnostics, and biosensors. The measurement of biological components in nanometers is not just a technical detail, but a fundamental aspect of how biology and nanotechnology merge to create new frontiers in medical science.