Question

(score for question 3: ___ of 10 points) 3. the distance to the sun is approximately 93,000,000 mi. a firefly is about 0.04 in. long. (a) what is the distance to the sun written in scientific notation? (b) what is the length of a firefly written in scientific notation? (c) the distance to the sun in inches is 5.89 × 10¹². how many fireflies would it take to reach the sun if they were put end to end? answer:

Explanation:

Step1: Convert 93,000,000 to scientific notation

Scientific notation is $a \times 10^n$ where $1 \leq a < 10$. Move decimal 7 places left: $9.3 \times 10^7$

Step2: Convert 0.04 to scientific notation

Move decimal 2 places right: $4 \times 10^{-2}$

Step3: Calculate number of fireflies

Divide sun distance (in inches) by firefly length: $\frac{5.89 \times 10^{12}}{4 \times 10^{-2}}$
Simplify: $\frac{5.89}{4} \times 10^{12 - (-2)} = 1.4725 \times 10^{14}$

Answer:

(a) $9.3 \times 10^7$ mi
(b) $4 \times 10^{-2}$ in
(c) $1.4725 \times 10^{14}$