MHB What is the percent magnification of the microscope?

[curtis2929]

A virus 3.0 X 10^-5 cm long appears to be 1.2cm long through a microscope. What is the percent magnification of the microscope?
Answer is 4000000. How did u get this answer?

 

[MarkFL]

Take the perceived length, divide by the actual length, and then multiply by 100 to get the percentage of magnification $M$:

$$M=\frac{1.2\text{ cm}}{3.0\E{-5}\text{ cm}}\cdot100=4000000$$

 

[curtis2929]

Tyvm. I'll try figure out how you got it:)

 

[MarkFL]

Tyvm. I'll try figure out how you got it:)

I just plugged the numbers into a calculator, but we could do it easily by hand:

$$M=\frac{1.2\text{ cm}}{3.0\E{-5}\text{ cm}}\cdot100$$

Cancel the cm units, and bring the 10 with the negative exponent up to the numerator with a positive exponent and use $100=10^2$:

$$M=\frac{1.2\E{5}}{3.0}\cdot10^2$$

Like bases, so add exponents:

$$M=\frac{1.2\E{7}}{3.0}$$

Multiply by $$1=\frac{10}{10}$$:

$$M=\frac{12\E{7}}{30}=\frac{12}{3}\E{6}=4.0\E{6}=4000000$$

 

[curtis2929]

Awesome I got it tyvm