Question

The diameter of the average cell in the human body is 1 x 10-5 meters. The diameter of a grain of sand is about 2 x 10-4 meters. The diameter of a human hair is about 0.000025 meters. Part A (2 points): What is the diameter of a human hair written in scientific notation? Part B (2 points): How many times longer is the diameter of a grain of sand than the diameter of the average cell in the human body? Show your work. Part C (2 points): Given that 1 meter = 1 x 109 nanometers, what is the diameter of the average cell in the human body, in nanometers? Show your work. Part D (2 points): The smallest known bacteria are from the genus Mycoplasma and can measure as small as 300 nanometers in diameter. Given that 1 meter = 1 x 109 nanometers, what is the diameter of the smallest bacteria, in meters? Give your answer in scientific notation and show your work. Part E (2 points): Very small numbers are often written in exponential form using scientific notation to make them easier to multiply or divide. Explain how to apply the laws of exponents when multiplying and dividing numbers written in scientific notation.

Answer 1

PART A:

Scientific notation is given by A×10ⁿ where A is any number in a unit and 'n' is an integer.

0.000025 = 2.5×10⁻⁵

PART B:

Diameter of grain of sand ÷ Diameter of human body average cell
(2×10⁻⁴) ÷ (1×10⁻⁵) 
(2÷1) × (10⁻⁴÷10⁻⁵)
2 × (10⁻⁴ ⁻ ⁻⁵) = 2 × 10⁽⁻⁴⁺⁵⁾ = 2 × 10¹ = 20 times bigger

PART C:

The diameter of human body's average cell in nanometer
1 × 10⁻⁵ metre = 1 × 10⁻⁵ × 10⁹ = 1 × 10⁽⁻⁵⁺⁹⁾ = 1 × 10⁴ nanometer

PART D:

Smallest bacteria = 300 nanometer
300 nm = 300 ÷ 10⁹ = (3 × 10²) ÷ 10⁹ = 3 × (10²⁻⁹) = 3 × 10⁻⁷ meter

PART E:

Laws of exponents that are applied in scientific notation is 

xᵇ × xᵃ = x⁽ᵇ⁺ᵃ⁾
xᵇ ÷ xᵃ = x⁽ᵇ⁻ᵃ⁾