Question

A human hair has an average diameter of 2.5 * 10 ^ - 5 meters. What is the maximum number of human hairs that could fit side by side (without overlapping) on a microscope slide that is 50 millimeters wide? Write your answer in scientific notation.

(A) 2 × 10 ^ 3

(B) 2 × 10 ^ 5

(D) 10 ^ - 3

(C) 2 × 10 ^ 6​

Answer 1

(A) 2 * 10^3.

Step-by-step explanation:

50 millimeters = 0.05 m

= 5 * 10^-2 meters.

So, we divide this by the diameter of 1 hair:

= (5 * 10^-2) / (2.5 * 10 ^ - 5)

= (5/2.5) * (10/^-2 / 10^-5)

= 2 * 10^(-2-(-5))

= 2 * 10^3.

Answer 2

Answer: Choice (A) 2 × 10^3

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Step-by-step explanation:

Let's find the width of the microscope slide in meters.

1000 mm = 1 m

1 mm = 1/1000 m

1 mm = 0.001 m

50*(1 mm) = 50*(0.001 m)

50 mm = 0.05 m

50 mm = 5 × 10^(-2) m

The microscope slide is 5 × 10^(-2) meters across. Divide this over the width of one hair.

5 × 10^(-2) ÷ 2.5 × 10^(-5)

(5/2.5) × 10^(-2 - (-5) )

2 × 10^(-2 + 5)

2 × 10^3

This converts to the number 2000. So we could have 2000 strands of hair side by side.