Metric Conversions
Problems #11 - 25

Return to Metric Table of Contents

Return to Metric Conversions


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) (109 nm / m) = 3.31 nm

    109 nm  
3.31 x 10¯9 m x ––––––– = 3.31 nm
    1 m  

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

(3.31 x 10¯9 m) (106 μm / m) = 3.31 x 10¯3 μm = 0.00331 μm

Note 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) (1012 pm / m) = 3.31 x 103 pm = 3310 pm

Notice 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 107 volts using a prefix.

Solution:

Examining a set of metric prefixes, we see that mega- (106) is the closest prefix, going in a "downward" direction. We need to convert our value in volts to the corresponding megavolt value:
(1 x 107 V) (1 MV / 106 V) = 10 MV

    1 MV  
1 x 107 V x ––––––– = 10 MV
    106 V  

Note 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) (106 μJ / 1 J) = 48 μJ

Note 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 1011 Hz using a prefix.

Solution:

From 1011, the next prefix in a downward direction is giga- (109)
(3.3 x 1011 Hz) (1 GHz / 109 Hz) = 330 GHz

    1 GHz  
3.3 x 1011 Hz x ––––––– = 330 GHz
    109 Hz  

Note that the unit of tera- (1012) is closer to the exponent in 1011, but we want the next unit smaller than our exponent. If we had converted to tera-, this is what would have resulted:

(3.3 x 1011 Hz) (1 THz / 1012 Hz) = 0.33 THz

0.33 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 m

Looking 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) (109 nm / 1 m) = 550 nm

Solution #2:

Ångstrom's original definition of what one Å equalled was this:
1 Å = 10¯8 cm

Suppose 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 cm

We 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) (104 μm / 1 cm) = 0.55 μm

Well, that didn't work. So, we try nano-:

(5.5 x 10¯5 cm) (107 nm / 1 cm) = 550 nm

Problem #16: Soon!


Return to Metric Table of Contents