Answer:
a. wide = 1 x 10^(-1) centimeters
height = 3 x 10^(-1) centimeters
depth = 5 x 10^(-2) centimeters
b. 1.5 x 10(-3) cubic centimeters.
c. 50 pieces
Explanation:
Part a.
We need to write 0.1, 0.3, and 0.05 in scientific notation, so
[tex]\begin{gathered} 0.1=1\times10^{-1} \\ 0.3=3\times10^{-1} \\ 0.05=5\times10^{-2} \end{gathered}[/tex]Where for example, the scientific notation of 0.05 has the form of 5 times a power of 10, where the exponent -2 means that the decimal point is 2 spaces to the left of 5.
Then, the answer is
wide = 1 x 10^(-1) centimeters
height = 3 x 10^(-1) centimeters
depth = 5 x 10^(-2) centimeters
Part b.
The volume of the eye of the needle can be calculated as the multiplication of its dimensions, so
[tex]\begin{gathered} \text{ Volume = Wide}\times\text{ Height}\times\text{ Depth} \\ \text{ Volume = \lparen1}\times10^{-1})\times(3\times10^{-1})\times(5\times10^{-2}) \\ \text{ Volume }=(1\times3\times5)\times(10^{-1}\times10^{-1}\times10^{-2}) \\ \text{ Volume }=\text{ 15}\times10^{-1-1-2} \\ \text{ Volume = 15 }\times10^{-4} \\ \text{ Volume = 0.0015} \end{gathered}[/tex]Then, this volume can be written in scientific notation as
[tex]0.0015=1.5\times10^{-3}[/tex]Therefore, the volume is 1.5 x 10(-3) cubic centimeters.
Part c.
To know the number of pieces that could fit in the eye of the needle, we need to divide the volume of the needle by the volume of each piece as follows
[tex]\begin{gathered} \text{ Number of pieces = }\frac{0.0015}{0.00003} \\ \\ \text{ Number of pieces = }\frac{1.5\times10^{-3}}{3\times10^{-5}} \\ \\ \text{ Number of pieces = 0.5}\times10^{-3-(-5)} \\ \text{ Number of pieces = 0.5}\times10^{-3+5} \\ \text{ Number of pieces = 0.5}\times10^2 \\ \text{ Number of piece = 50} \end{gathered}[/tex]Therefore, the answer is 50 pieces.