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For Example 3.2, how do I do the math?
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In the first part of this example, you have:

(405 nm/1) x (10-9 m/1nm)

When you multiply 405 by 10-9, you get

405 x 10-9

This is not standard scientific notation, because there is no decimal place in 405. To get it into scientific notation, move the decimal to the left 2 places. This decreases 405 by a factor of 100. To keep the value of the entire number the same, then, you must INCREASE 10-9 by 100. Increasing 10-9 by 100 gives you 10-7. Thus, it is 4.05 x 10-7 m.

In the next step, you have

(3.0 x 108 m/s) / (4.05 x 10-7 m)

You can divide the two numbers first:

3.0 / 4.05 = 0.74

You can then divide the two exponents. When multiplying numbers with exponents, you ADD the exponents. When dividing numbers with exponents, you SUBTRACT the exponents:

108 / 10-7 = 10(8 – -7) = 1015

Thus, you have an answer of 0.74 x 1015. Once again, this is not standard scientific notation. To get it into standard scientific notation, multiply 0.74 by 10 to get 7.4. This means you must divide 1015 by 10 to get 1014. Thus, the answer is:

7.4 x 1014 1/s

Now, having done all that, if you have a scientific calculator, it allows you to input the numbers in scientific notation and it does all of this for you. If you have a scientific calculator, read the manual to find out how to do this or you might be able to find a YouTube video explaining how to do it.

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