Converting units and solving proportions show up all through the TEAS math section, and they matter just as much once you start a health program: doses, fluid volumes and patient weights all depend on them. The good news is that one method handles almost every one of these problems.
The one method: multiply by a fraction equal to 1
A conversion factor such as 1 kg = 1,000 g can be written as a fraction equal to 1, either 1,000 g / 1 kg or 1 kg / 1,000 g. Multiplying by 1 never changes a quantity's size, only its units. Pick the version that puts the unit you want to remove in the denominator, so it cancels.
Example 1. Convert 2.4 kg to grams.
2.4 kg × (1,000 g / 1 kg) = 2,400 g. The kilograms cancel, leaving grams.
Conversions worth knowing
| Within the metric system | Between systems |
|---|---|
| 1 kg = 1,000 g | 1 in = 2.54 cm (exact) |
| 1 g = 1,000 mg | 1 lb ≈ 0.454 kg (1 kg ≈ 2.2 lb) |
| 1 L = 1,000 mL | 1 fl oz ≈ 29.57 mL (often rounded to 30 mL) |
| 1 m = 100 cm = 1,000 mm | 1 mi ≈ 1.609 km |
In the US customary system, 1 ft = 12 in, 1 yd = 3 ft, 1 lb = 16 oz, 1 cup = 8 fl oz and 1 qt = 4 cups. Within the metric system every step is a power of 10, so a conversion is just a move of the decimal point.
Example 2. A patient weighs 165 lb. What is the weight in kilograms, to the nearest tenth, using 1 kg = 2.2 lb?
165 lb × (1 kg / 2.2 lb) = 75.0 kg. Dividing by 2.2 makes sense: a kilogram is heavier than a pound, so the number of kilograms must be smaller.
Chaining conversions
When no single factor gets you there, line up several so each unit cancels in turn.
Example 3. How many milliliters are in 3 cups?
3 cups × (8 fl oz / 1 cup) × (29.57 mL / 1 fl oz) ≈ 709.7 mL, or 720 mL if the problem tells you to use 30 mL per fluid ounce. Always use the factor the question gives you; answer choices are built on it.
Proportions: set up two equal ratios
A proportion says two ratios are equal. Write both ratios with the same units in the same positions, then cross-multiply.
Example 4. A medicine contains 250 mg in every 5 mL. How many milliliters hold 400 mg?
250 mg / 5 mL = 400 mg / x mL. Cross-multiply: 250x = 2,000, so x = 8 mL.
Example 5. A map's scale is 2 cm to 15 km. Two towns are 7 cm apart on the map. How far apart are they?
2 cm / 15 km = 7 cm / x km. Then 2x = 105, so x = 52.5 km.
Check that the answer is sensible
Before choosing an answer, ask whether its size makes sense. Converting to a smaller unit (kilograms to grams, liters to milliliters) must give a bigger number. In Example 4, 400 mg is more than 250 mg, so the answer must be more than 5 mL. A quick check like this catches most set-up errors.
Common mistakes
- Writing the conversion factor upside down, so the units multiply instead of cancel.
- Moving the decimal point the wrong way in a metric conversion.
- Mixing units inside a proportion, such as milligrams on top of one ratio and milliliters on top of the other.
- Rounding in the middle of a chained conversion instead of only at the end.
- Using a remembered conversion factor when the question gives a different one.
Practice TEAS math questions, with the working shown in every explanation.
Source: the ATI TEAS Version 7 Content Outline (ATI), math objectives on proportions, ratios and unit conversion; conversion definitions from NIST. passvana is independent and is not affiliated with ATI.