Question

DNA of the Human Body If completely unraveled, all of a human's DNA would be able to reach a distance of nearly \(3.2 \times 10^{5} \mathrm{~km}\), the distance from Earth to the moon. Given that each base pair in a DNA helix extends a distance of \(3.4 \AA\), calculate the number of base pairs found within the entirety of a human's DNA.

Short answer

The total number of base pairs is approximately \(9.41 \times 10^{17}\).

Step-by-step solution

Understanding the Units

First, we need to understand the units involved in the problem. The total length of the DNA is given in kilometers, while the extension of each base pair is given in angstroms (\(\text{Å}))\). We need to convert these numbers to a common unit for accurate computation.

Convert Length from Kilometers to Angstroms

1 kilometer is equal to \(10^{13}\) angstroms. Therefore, we can convert \(3.2 \times 10^{5} \text{ km}\) to angstroms:\[3.2 \times 10^{5} \text{ km} = 3.2 \times 10^{5} \times 10^{13} \, \text{Å} = 3.2 \times 10^{18} \, \text{Å}\]

Calculate the Number of Base Pairs

Now that we have converted the total length of the DNA to angstroms, we can determine the number of base pairs. Each base pair extends \(3.4\ \, \text{Å}\). Therefore, to find the number of base pairs:\[\frac{3.2 \times 10^{18} \, \text{Å}}{3.4 \, \text{Å/base pair}} = \frac{3.2}{3.4} \times 10^{18} \, \text{base pairs} \approx 0.941 \times 10^{18} \, \text{base pairs}\]

Simple Calculation

Calculate the value of \(0.941 \times 10^{18}\):\[0.941 \times 10^{18} \approx 9.41 \times 10^{17}\ \, \, \text{base pairs}\]

Key concepts

Base Pairs

When we talk about DNA, one crucial aspect to understand is the concept of base pairs. DNA, or deoxyribonucleic acid, is structured as a double helix. This double helix is composed of two strands that are held together by base pairs. Base pairs are formed by the bonding of specific nucleotides: adenine with thymine, and guanine with cytosine.
In this problem, base pairs play a key role because we're looking at how they repeat along the DNA to give it length. Each base pair provides a measure of length for the DNA helix. They are like building blocks that repeat over and over, ultimately defining the structural length of the DNA strand.
This exercise simplifies the complexity of DNA by representing its length through these repeating units. Understanding base pairs helps us appreciate how a seemingly small structure can be mapped out to cover an immense length.

Angstrom Conversion

Converting units is essential when working with DNA strand measurements, as in this example. An angstrom (\( \text{Å} \)) is a unit of length that is commonly used to measure things at an atomic scale, such as bonds and DNA base pairs. One angstrom equals \( 10^{-10} \) meters. In contrast, larger dimensions like the total length of all human DNA can be given in kilometers.

• To solve the problem accurately, we need to convert kilometers to angstroms.
• This requires understanding conversion factors – specifically \(1 \text{ km} = 10^{13} \text{ Å} \).

By converting, we change the total length of DNA from kilometers to angstroms. This gives us a consistent unit of measurement to calculate how many base pairs fit the given length. While conversions might seem tedious at first, they simplify complex multiscale problems significantly.

Step-by-Step Problem Solving

Breaking down problems into steps is a key approach to effective problem-solving. The original solution provides a perfect example of a clear, methodical process. Start by understanding the given units, which is fundamental, as mismatched units can lead to erroneous conclusions.
Next, convert the units so that they match across the problem context. This step narrows down discrepancies and sets the ground for accurate calculations. Once the units are harmonized, focus on solving the main question, which is calculating the number we seek – in this case, how many base pairs fit into a given length of DNA.
Finally, execute the calculation with attention to detail. Once you reach a conclusion like \(0.941 \times 10^{18}\), simplify if necessary to provide a clear and concise answer. This method is an excellent way to tackle a variety of scientific problems, not just those related to DNA.