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