Converting from One Metric Unit to Another

practice problems are at the bottom of page

TUTORIAL:

Skills you need to do this include:

1) memorize the metric prefixes names and symbols
2) determine which of two prefixes represents a larger amount
3) determine the exponential "distance" between two prefixes
4) significant figure rules
5) scientific notation

Here are two typical metric conversion problems:

1) Convert 2.50 mg to picograms.
2) Convert 0.080 cm to km.

A slightly more complex one is:

3)  Convert the speed of light (2.998 x 108 m/sec) to km/hr.

The key skill in solving these problems is to construct a conversion factor. This conversion factor will make the old unit go away (micrograms and km in the top two examples) and create the new unit (pm and cm) in its place. Along with this change, there will be a change in the value of the number.

Let's focus on the first example: Convert 2.50 mg to picograms. Since there isn't a direct conversion between mg and pg, two conversions will be needed.

STEP ONE: Write the value (and its unit) from the problem, then in order write: 1) a multiplication sign and a fraction bar, 2) a second multiplication sign and fraction bar, 3) an equals sign, and 4) the unit in the answer. Put a gap between 3 and 4. All that looks like this:

2.50 µg × ______________  × ________________ =         pg

The fraction bars will have the conversion factors. There will be a number and a unit in the numerator and the denominator.

STEP TWO: Write the unit from the problem in the denominator of the first conversion factor, like this:

STEP THREE: Since two conversions are needed, write the base unit in the numerator of the first conversion factor.

STEP FOUR: Using the metric conversion definitions, place the definition of micro (m) next to the base unit (g), and a one next to the abbreviation (mg). The bigger unit (g) will always have a smaller number in front compared to the small unit (mg).

STEP FIVE: Place the base unit in the denominator and the final unit in the numerator for the last conversion.

STEP SIX: Using the metric conversion definitions, place the definition of pico (p) next to the base unit (g), and a one next to the abbreviation (pg). The bigger unit (g) will always have a smaller number in front compared to the small unit (pg).

Now, multiply and put into proper scientific notation format. The answer should be 2.50x106 pg.  Make sure the new unit is present after the answer. Sometimes, the exponential number is in the denominator. You must move it to the numerator and when you do so, remember to change the sign. Also, DO NOT move the unit with it. That unit has been cancelled and is no longer there.

You can also write the metric conversion factors with ones in front of the base unit. If you do this, the exponent in front of the metric abbreviation will always be a positive exponent.

Why a one in front of the larger unit? Some people find it easier to visualize how many small parts make up one bigger part, like 1000 m make up one km or 1,000,000 mg make up one g. Going the other way, visualizing what part a larger unit is of one smaller unit, is possible, but requires more sophistication. For example, how many meters are in one nanometer? The answer is 0.000000001 or 10¯9. You may be able to handle the conversion and that is just fine. Using 1 m = 1,000,000,000 nm might be easier for some students.

For the other 2 problems, here are the solutions:

Practice Problems work these out on paper, check answers later!
(the worked solutions use kind of a goofy conversion method, so just look at the answers)

1. 0.75 kg to milligrams

2. 1500 millimeters to km

3. 2390 g to kg

4. 0.52 km to meters

5. 65 kg to g

6. 750 micrograms to g

7. 0.25 megameters to cm

8. 23.8 fg to kg   (you don't need to memorize femto, but look it up in the text)

9. 2.77 kg to mg

10. 2.90 cm to terameters    (you don't need to memorize tera, but look it up in the text)

11. 45.6 microliters to megaliters

12. 1.08 kg to mg

13. 9.57 x 10¯8 mm to nanometers

14. 2.00 L to mL

15. 35.28 mL to L