Question

Dna is approximately 2.5 nm in length. of an average man is 5 ft 10 in. tall, how many dna molecules could be stacked to extend from the ground to the top of the head of an average man?

Answer 1

There are 7 × 10⁸ or 700 million DNA molecules in an average man.

FURTHER EXPLANATION

This is a unit conversion problem. In order to get the number of DNA molecules, the height of the man should first be converted into nm. It would require multiple steps to do this.

For the provided solution, the following conversion factors are used:

12 in =  1 foot

1 in = 2.54 cm

1 m = 100 cm

1 m = 10⁹ nm

First, convert the height into inches.

$height = 5 \ ft \times \frac{12 \ in}{1 \ ft} = 60 \ in$

The height is 5 ft 10 inches. 5 feet is equivalent to 60 inches. Therefore, the average man is 70 inches tall.

Convert height in inches to nm.

Since the DNA molecules are measured in nanometers, it is necessary to determine how tall the man is in nanometers.

$height \ in \ nm \ = 70 \ in \times \frac{2.54 \ cm}{1 \ in} \times \frac{1 \ m}{100 \ cm} \times \frac{10^9 \ nm}{1 \ m}\\\\\boxed {height \ in \ nm \ = 1.778 \times 10^{9} \ nm}$

Determine the number of DNA molecules.

To find the number of DNA molecules it would be required to calculate how many 2.5 nm molecules could be stacked together to a total height of 1.778 × 10⁹ nm.

$number \ of \ DNA \ molecules \ = 1.778 \times 10^{9} \ nm \ \times \frac{1 \ molecule}{2.5 \ nm} \\\\\boxed {number \ of \ DNA \ molecules \ = 7.112 \times 10^8 \ molecules}$

Since the least number of significant figures in the given is 1, the answer should have one significant figure also. Hence, the final answer is:

$\boxed {\boxed {number \ of \ DNA \ molecules \ = 7 \times 10^{8} \ molecules}}$

LEARN MORE

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Keywords: DNA, conversion

Answer 2

To determine the number of dna molecules that can be stacked as requested in this item, we convert the given measurements in a single unit. For simplicity, we convert all the lengths to meters.

Length of DNA molecule = (2.5 nm)(1 x 10^-9 m/1 nm) = 2.5 x 10^-9 nm

Height of a person = (5 ft 10 in)(12 inches/ 1ft)(2.54 cm/1 in)(1 x 10^-2 m/ 1 cm)
               = 1.778 m

Then, divide the height of the person by the length of a single DNA molecule.

       n = 1.778 m / (2.5 x 10^-9)
       n = 7.112 x 10^8

Hence, the number of DNA would be 7.112 x 10^9.