Problems #11 - 25

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There is an unstated goal in the first five problems of this section:

to have the numerical part be not less than 1 and not greater than 1000.

In other words, you're not going to any old metric prefix you want. You're going to one that will cause the numerical portion to be between 1 and 1,000. (You sometimes see it given as between 1 and 999.)

Please keep in mind that this goal is almost always not stated in the problem.

**Problem #11:** Express 3.31 x 10¯^{9} m using a prefix.

**Solution:**

The correct answer to the above is 3.31 nm. Here's how (formatted two different ways, you need to be familiar with both):

(3.31 x 10¯^{9}m) (10^{9}nm / m) = 3.31 nm

10 ^{9}nm3.31 x 10¯ ^{9}mx ––––––– = 3.31 nm 1 m

If you selected micro- (the prefix before nano-), this is the answer:

(3.31 x 10¯^{9}m) (10^{6}μm / m) = 3.31 x 10¯^{3}μm = 0.00331 μmNote that the numerical value is 1000 times smaller than the correct answer.

If you selected pico- (the prefix after nano-), you get this:

(3.31 x 10¯^{9}m) (10^{12}pm / m) = 3.31 x 10^{3}pm = 3310 pmNotice that the numerical value is 1000 times greater than the correct answer

Using micro- and pico- both satisfy the exact wording of the problem, but they both fail the unstated part.

**Problem #12:** Express 1 x 10^{7} volts using a prefix.

**Solution:**

Examining a set of metric prefixes, we see that mega- (10^{6}) is the closest prefix, going in a "downward" direction. We need to convert our value in volts to the corresponding megavolt value:(1 x 10^{7}V) (1 MV / 10^{6}V) = 10 MV

1 MV 1 x 10 ^{7}Vx ––––––– = 10 MV 10 ^{6}VNote that it is the closest prefix less than (or equal to) the exponent in the value in the problem.

**Problem #13:** Express 4.8 x 10¯^{5} Joules using a prefix.

**Solution:**

Look at the 10¯^{5}. We want the next prefix going "downward" in a list of metric prefixes.That prefix is micro- (10¯

^{6})We convert from J to μJ:

(4.8 x 10¯^{5}J) (10^{6}μJ / 1 J) = 48 μJNote that this "downward" direction is in reference to a list of metric prefixes having the positive exponents listed first and the proceeding to the negative exponents. This link shows an example of what I mean.

**Problem #14:** Express 3.3 x 10^{11} Hz using a prefix.

**Solution:**

From 10^{11}, the next prefix in a downward direction is giga- (10^{9})(3.3 x 10^{11}Hz) (1 GHz / 10^{9}Hz) = 330 GHz

1 GHz 3.3 x 10 ^{11}Hzx ––––––– = 330 GHz 10 ^{9}HzNote that the unit of tera- (10

^{12}) is closer to the exponent in 10^{11}, but we want the next unitsmallerthan our exponent. If we had converted to tera-, this is what would have resulted:(3.3 x 10^{11}Hz) (1 THz / 10^{12}Hz) = 0.33 THz0.33 fails the stipulation that the numerical value must be greater than (or equal to) 1.

**Problem #15:** Express 5500 Ångstroms (symbol is Å) using a prefix.

**Solution #1:**

This is a bit of an odd one because Å is not a SI-unit. However, we can express Å using a SI-unit:(5500 Å) (10¯^{10}m / 1 Å) = 5.5 x 10¯^{7}mLooking at the exponent in 10¯

^{7}, we select nano- (10¯^{9}) as the next unit in the downward (or smaller) direction:(5.5 x 10¯^{7}m) (10^{9}nm / 1 m) = 550 nm

**Solution #2:**

Ångstrom's original definition of what one Å equalled was this:1 Å = 10¯^{8}cmSuppose you were given that conversion in the body of the problem. What to do?

You could convert 10¯

^{8}cm / Å to 10¯^{10}m / Å and continue with solution #1. Suppose you didn't. What to do?Let's convert and see what happens:

(5500 Å) (10¯^{8}cm / Å) = 5.5 x 10¯^{5}cmWe have an exponent, but we do not have a numerical value between 1 and 1000, so we have to keep converting. Hopefully, you can see that moving to the next smaller prefix (milli-) isn't sufficient. Perhaps, going to micro- would work:

(5.5 x 10¯^{5}cm) (10^{4}μm / 1 cm) = 0.55 μmWell, that didn't work. So, we try nano-:

(5.5 x 10¯^{5}cm) (10^{7}nm / 1 cm) = 550 nm

**Problem #16:** Soon!