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Using these two pieces of knowledge, here are the steps to converting a measurement from one unit into another, using the example problem above of converting 2.3 square miles into acres:

Step 1. Write down the given units as a fraction over 1.


Step 2. To the far right of this fraction, write an "=" sign and a fraction line. Put the units of the final answer in the numerator. Except for a "1" in the numerator, no numbers should be in this fraction yet.

=


Step 3. Write down conversion factors. Since we know the relationship between square miles and acres (1 sq. mi. = 640 acres), we can write down 2 conversion factors:


and


Step 4. Multiply a conversion factor into the equation. In order to cancel out, the denominator of the conversion factor must have the same units as the numerator of the given fraction (the fraction on the left of the equation). In this case, the conversion factor must have "sq mi" in the denominator. Multiply the fraction on the left by the conversion factor:

× =


Step 5. Cancel out the units and multiply:

× = 1, 472 acres


Step 6. Round the answer to the same number of significant digits as the original number (for now, we will treat our conversion factors as if they are precise). 2.3 has 2 significant digits. 1,472 acres = 1,500 acres. Thus, 2.3 sq mi = 1,500 acres.

To convert between English and Metric units, it is useful to know the following conversion factors:

Length/Area

1 in = 2.540 cm
1 ft = 0.3048 m
1 mi = 1.609 km
1 sq ft = 0.0929 sq m
1 sq mi = 2.59 sq km

Capacity

1 fl oz = 29.575 ml
1 gal = 3.785 l

Weight

1 oz = 28.35 g
1 lb = 0.4536 kg

Here is an example of a conversion from metric units to English units: if Bob ran a 5.0 km race, how many miles did he run?

Step 1. Write down the given units as a fraction over 1.


Step 2. To the far right of this fraction, write an "=" sign and a fraction line. Put the units of the final answer in the numerator. Except for a "1" in the numerator, no numbers should be in this fraction yet.

=


Step 3. Write down conversion factors. Since we know the relationship between kilometers and miles (1 mi = 1.609 km), we can write down 2 conversion factors:


and


Step 4. Multiply a conversion factor into the equation. In order to cancel out, the denominator of the conversion factor must have the same units as the numerator of the given fraction (the fraction on the left of the equation). In this case, the conversion factor must have "km" in the denominator. Multiply the fraction on the left by the conversion factor:

× =


Step 5. Cancel out the units and multiply:

× = = 3.1075 mi


Step 6. Round the answer to the same number of significant digits as the original number. 5.0 has 2 significant digits. 3.1075 mi = 3.1 mi. Thus, 5.0 km = 3.1 mi.