Go to some one-unit Metric conversions

Go to some two-unit Metric conversions

Go to Metric-English Conversion Problems #1-10

Go to Metric-English Conversion Problems #11-25

The conversions between Metric and English units are not all exact (meaning defined) values (like, say, 1 meter = 100 cm). Consequently, a question that often arises is how to determine significant figures in the answer. The solution to this is to use as many digits as possible in any Metric-English conversion unit. For example, I tend to use 453.6 g/lb when converting between grams and pounds, but you could use 453.592 g/lb, if it were needed.

Put another way, what you do is look to use more significant figures in your conversions than are present in your starting value. Then, make sure to carry two or three guard digits through each calculation (if you do a several-step calculation) and round off to the final number of significant figures only when you arrive at the final answer.

You may want to search the Internet for information on Metric-English conversions. I will include discussion of a variety of conversions in most of the solutions provided below. For example, see the end of Example #1 for a mention about the consequence of one inch equalling 2.54 cm by definition.

In the examples to follow, I will freely mix one-unit and two-unit conversions as well as conversions involving square and cube units.

**Example #1:** Convert 1.000 km to inches.

**Solution:**

1) A conversion that you should memorize is this:

1 inch = 2.54 cm2) Based on that, I propose to first change km to cm (which is a common Metric-only conversion):

1.000 km times (103) Now, the conversion to inches:^{5}cm / km) = 1.00 x 10^{5}cm

1.00 x 10^{5}cm times (1 inch / 2.54 cm) = 39370 inchSince 1 inch = 2.54 cm is by definition, I propose to keep four sig figs in the answer. In other words, 2.54 is NOT three sig figs. Since it is a defined value, it plays no role in determining the number of significant figures. Some teachers will state that the defined value has an infinite number of significant figures. The ChemTeam prefers to state that defined values play no role.

**Example #2:** Convert 4.04 x 10^{5} feet to centimeters

**Solution:**

1) Convert feet to inches:

4.04 x 10^{5}feet x (12 inches / ft) = 4.848 x 10^{6}in

2) Convert inches to centimeters:

4.848 x 10^{6}in x (2.54 cm / in) = 1.23 x 10^{7}cm (to three sig figs)

3) Here is the problem, done in one line:

Remember, this is what is commonly meant by saying "dimensional analysis." All the conversions are strung together in one line, as opposed to be set out as a multi-step solution, as was done in Example #1 and in steps 1 and 2 to this example.

**Example #3:** Convert 1.000 yards to nanometers.

**Solution:**

**Example #4:** Convert 0.02515 ft^{3} to cm^{3}

**Solution #1:**

1) Convert 1 foot to inches, then centimeters:

1 foot = 12 inches (by definition)12 inches x (2.54 cm / 1 inch) = 30.48 cm

2) Calculate what one cubic foot would be in cubic centimeters:

30.48 cm x 30.48 cm x 30.48 cm = 28317 cm^{3}

3) Determine answer to problem:

0.02515 ft^{3}x (28317 cm^{3}/ ft^{3}) = 712.2 cm^{3}

Now, go to Google and type this in the search box:

convert 0.02515 cubic foot to cubic centimeters

and then press "Return."

**Solution #2:**

1) Think of the volume in this manner:

0.02515 ft^{3}= 0.02515 ft x 1 ft x 1 ft

2) Now, convert it to cubic inches:

(0.02515 ft x 12 in/ft) x 12 in x 12 in = 43.4592 in^{3}

3) Think of 43.4592 in^{3} this way:

43.4592 in^{3}= 43.4592 in x 1 in x 1 in

4) Convert to cm:

(43.4592 in x 2.54 cm/in) x 2.54 cm x 2.54 cm = 712.2 cm^{3}

**Example #5:** The three dimensions of a box are measured to be 1.3 in, 3.4 in, and 5.9 in. What is the volume of the box in liters?

**Solution:**

1) Calculate volume of the box in cm^{3}:

(1.3 in x 3.4 in x 5.9 in) times (2.54 cm / in)^{3}427.342 cm

^{3}

2) Convert cm^{3} to mL, then to liters:

427.342 cm^{3}= 427.342 mL427.342 mL times (1 L / 1000 mL) = 0.427 L

To two sig figs, this is 4.3 x 10

^{-1}LI had to use scientific notation for the answer because expressing the volume as 0.430 L would have been three sig figs.

Comment: for step one, I could have written this:

(1.3 in x 2.54 cm / in) x (3.4 in x 2.54 cm / in) x (5.9 in x 2.54 cm / in)The above simply converts each inch value separately. In step one above, the units would have been written this way:

(in

^{3}times cm^{3}/in^{3})

**Bonus Problem:** How many slugs are there in 54.29 kg?

Hint: use Google to convert slugs to kilograms

A slug is a very old-school unit of mass. The ChemTeam has heard of it (as well as dyne and erg), but has never used it in a computation, either as a student or as a teacher.

The ChemTeam would shout "Erg!" when putting the shot in high school and college. He thought this was quite funny, knowing that the erg is a unit of energy.

The ChemTeam is easily amused!

Go to Metric-English Conversion Problems #1-10

Go to Metric-English Conversion Problems #11-25

Go to some one-unit Metric conversions