The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. Its body shape can be modeled as a 2-μm-long cylinder with a 1 μm diameter, and it has a mass of 1×10^−12g. Its chromosome consists of a single double-stranded chain of DNA 700 times longer than its body length. The bacterium moves at a constant speed of 20 μm/sμm/s though not always in the same direction. Required:
a. What is its mass?
b. What is the length of its DNA, in millimeters?

(a) the mass is 1× kg

(b) length of the DNA in millimeters is 1.4 mm

(a) Given that the mass of the organism in grams is 1× g

to convert it to kilograms we multiply it by since 1 g = kg

therefore mass = 1× × kg = 1× kg

(b) according to the question, the DNA is 700 times the body length of the organism. the body length of the organism is 2× m

so the length of DNA, let's say L = 700×2× m

⇒ L = 14×m

to convert it in millimeters we multiply it by , since 1 m = mm

   L = 14× × mm = 1.4 mm

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A) Mass = 1 × 10^(-15) kg

B) DNA length = 1.4 mm

Explanation:

A) We are given its mass as; mass = 1 × 10^(−12) g

Now we will convert it to kg.

From conversions, 1000 g = 1 kg

Thus;1 × 10^(−12) g = (1 × 10^(−12))/1000 = 1 × 10^(-15) kg

Mass = 1 × 10^(-15) kg

B) We are given its length to be 2 μm long.

So we will convert to m first then mm.

To convert to m, we know that μm = 10^(-6) m

Thus;

Length = 2 × 10^(-6) m

Also, from conversions, 1m = 1000 mm

Thus;

2 × 10^(-6) m will give;

2 × 10^(-6) × 1000 mm = 2 × 10^(-3) mm

Length = 2 × 10^(-3) mm

Also, we are told that DNA 700 times longer than its body length.

Thus,

DNA length = 700 × 2 × 10^(-3) mm = 1.4 mm