Question

The eye of a needle is 0.1 centimeter wide, 0.3 centimeter tall, and 0.05 centimeter deep.a. Write the dimensions in scientific notationb. Find the volume of the eye of the needle, assuming it is rectangular. Write your answer in scientific notation.c. An artist installs minuscule bits of glass, each of which has a volume of 0.00003 cubic centimeter. How many pieces could fit in the eye of the needle?

Answer 1

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

Step-by-step explanation:

Part a.

We need to write 0.1, 0.3, and 0.05 in scientific notation, so

`\begin{gathered} 0.1=1*10^(-1) \\ 0.3=3*10^(-1) \\ 0.05=5*10^(-2) \end{gathered}`

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

`\begin{gathered} \text{ Volume = Wide}*\text{ Height}*\text{ Depth} \\ \text{ Volume = \lparen1}*10^(-1))*(3*10^(-1))*(5*10^(-2)) \\ \text{ Volume }=(1*3*5)*(10^(-1)*10^(-1)*10^(-2)) \\ \text{ Volume }=\text{ 15}*10^(-1-1-2) \\ \text{ Volume = 15 }*10^(-4) \\ \text{ Volume = 0.0015} \end{gathered}`

Then, this volume can be written in scientific notation as

`0.0015=1.5*10^(-3)`

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

`\begin{gathered} \text{ Number of pieces = }(0.0015)/(0.00003) \\ \\ \text{ Number of pieces = }(1.5*10^(-3))/(3*10^(-5)) \\ \\ \text{ Number of pieces = 0.5}*10^(-3-(-5)) \\ \text{ Number of pieces = 0.5}*10^(-3+5) \\ \text{ Number of pieces = 0.5}*10^2 \\ \text{ Number of piece = 50} \end{gathered}`

Therefore, the answer is 50 pieces.