A human cell has 10 ^14 cells and each cell has about 6.4 x 10 ^9 nucleotide pairs of DNA. What is the length, in cm, of double helix that can be formed from the total amount of DNA in a human individual?
To find the total length of the double helix DNA in a human individual, we can calculate the product of the number of cells and the number of nucleotide pairs per cell.
Given:
Number of cells = 10^14
Number of nucleotide pairs per cell = 6.4 x 10^9
To calculate the total length of the double helix DNA, we can multiply these two values together:
Total length = Number of cells × Nucleotide pairs per cell
Total length = (10^14) × (6.4 x 10^9)
To simplify the calculation, we can write this in scientific notation:
Total length = (10^14) × (6.4 x 10^9)
= 10^(14+9+log(6.4))
Using the log calculator, we find that log(6.4) is approximately 0.806180 / 0.9030908.
Total length = 10^(14+9+log(6.4))
= 10^(23+0.806180)
= 10^23 × 10^0.806180
≈ 10^23 × (6.4)
Now we can evaluate this expression:
Total length ≈ 6.4 x 10^23
Since 1 turn of the DNA double helix is about 3.4 nm (roughly 1.34 x 10^-7 inches) long, we can convert this into centimeters:
Total length = 6.4 x 10^23 x (1.34 x 10^-7) cm
When we multiply these values together, we get:
Total length ≈ 8.576 x 10^16 cm
Therefore, the length of the double helix that can be formed from the total amount of DNA in a human individual is approximately 8.576 x 10^16 centimeters.
To find the length of the double helix that can be formed from the total amount of DNA in a human individual, we need to calculate the total length of the DNA strands and then multiply it by two (since DNA has a double helix structure).
Let's break down the calculation step-by-step:
1. Calculate the total amount of DNA:
A human cell has 10^14 cells, and each cell has about 6.4 x 10^9 nucleotide pairs of DNA.
Therefore, the total amount of DNA would be: 10^14 cells * 6.4 x 10^9 nucleotide pairs/cell.
2. Convert nucleotide pairs to nucleotides:
Each nucleotide pair consists of two nucleotides. To find the total number of nucleotides, we need to multiply the number of nucleotide pairs by 2. So, the total number of nucleotides would be: 2 * (10^14 cells * 6.4 x 10^9 nucleotide pairs/cell).
3. Calculate the length of the DNA:
The length of a single nucleotide is approximately 0.34 nanometers.
Therefore, to convert the total number of nucleotides to centimeters, we need to multiply it by the length of a nucleotide and convert it from nanometers to centimeters. Thus, the length of the DNA would be: 2 * (10^14 cells * 6.4 x 10^9 nucleotide pairs/cell) * 0.34 x 10^(-7) cm.
4. Simplify the equation:
Multiply the values inside the brackets and simplify the scientific notation to get the final result.
Using these steps, you can calculate the length of the double helix that can be formed from the total amount of DNA in a human individual.