3. Use the fact that $\sqrt{7}$ is a solution to the equation $x^{2}=7$ to find a decimal approximation of $\sqrt{7}$ whose square is between 6.9 and 7.1 .
4. Graphite is made up of layers of graphene. Each layer of graphene is about 200 picometers, or $200 \times 10^{-12}$ meters, thick. How many layers of graphene are there in a 1.6-mm-thick piece of graphite? Express your answer in scientific notation.
(From Unit 7, Lesson 14.)
Answer
boxed{Question 4: 8 \times 10^6}
Step 1 ：Find the decimal approximation of \(\sqrt{7}\) by taking the average of the square roots of the lower and upper bounds: \(\frac{\sqrt{6.9} + \sqrt{7.1}}{2} \approx 2.6457\)
Step 2 ：Divide the thickness of the graphite by the thickness of a single layer of graphene to find the number of layers: \(\frac{0.0016}{2 \times 10^{-10}} = 8 \times 10^6\)
Step 3 ：boxed{Question 3: 2.6457}
Step 4 ：boxed{Question 4: 8 \times 10^6}
