A speck of dust is 1.25 x 10^2 millimeters wide. The image in an electron microscope is 3 x 10^2 times larger than the actual size. How many millimeters wide is the image of the speck of dust?

Question

A. 375
B. 3,750
C. 37,500
D. 375,000

Answer 1

To find the width of the image of the speck of dust, we need to multiply the actual width of the speck of dust by the magnification factor of the electron microscope.

1. The actual width of the speck of dust is \(1.25 \times 10^2\) millimeters.
2. The magnification factor is \(3 \times 10^2\).

Now we can calculate the width of the image:

\[ \text{Width of image} = (\text{Width of speck}) \times (\text{Magnification}) \]

Substituting the given values:

\[ \text{Width of image} = (1.25 \times 10^2) \times (3 \times 10^2) \]

To multiply these, we can multiply the coefficients and the powers of ten separately:

\[ = (1.25 \times 3) \times (10^2 \times 10^2) \]

Calculating the coefficients:

\[ 1.25 \times 3 = 3.75 \]

For the powers of ten:

\[ 10^2 \times 10^2 = 10^{2+2} = 10^4 \]

Combining both results:

\[ = 3.75 \times 10^4 \]

Now converting \(3.75 \times 10^4\) into standard decimal form:

\[ 3.75 \times 10^4 = 37500 \]

Thus, the width of the image of the speck of dust is 37,500 millimeters.

Therefore, the answer is:

C. 37,500