Question

The smallest object visible with your eyes is similar to the width of a piece of hair, which is 1×10−4 meters wide. Using an optical microscope, you can see items up to 2×10−7 meters wide. How much larger are objects you can see with your eyes than objects you can see with an optical microscope? A 0.2×10−3 times larger B 5×102 times larger C 0.5×103 times larger D 2×10−3 times larger

Answer 1

B.
`5*10^(2)`

Explanation:

We are told that the smallest object visible with our eyes is similar to the width of a piece of hair, which is
`1* 10^(-4)` meters wide.

Using an optical microscope, we can see items up to
`2* 10^(-7)` meters wide.

To find the objects we can see with our eyes are how much larger than the objects we can see with an optical microscope, we can set an equation as:

`\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=(1*10^(-4))/(2*10^(-7))`

Using the exponent rule of quotient
`(a^m)/(a^n)=a^(m-n)` we will get,

`\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=(1)/(2)*10^(-4-(-7))`

`\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10^(-4+7)`

`\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10^(3)`

`\frac{\text{The width of the object we can see with our eyes}}{\text{The width of the objects we can see with microscope}}=0.5*10* 10^(3-1)`

`\text{The object we can see with our eyes}=5*10^(2)*\text{The objects we can see with microscope}`

Therefore, the objects we can see with our eyes are
`5*10^(2)` times larger than the objects we can see with an optical microscope and option B is the correct choice.