How to convert units without guessing: metric, US and health-care units
TEAS 7 outline: Convert units within and between US standard and metric systems
Also covers HESI A2 Math (Household and metric measures)
- Each metric step is a factor of 10, so just move the decimal.
- A smaller unit gives a bigger number: 0.4 g = 400 mg.
- Divide pounds by 2.2 to get kilograms.
- 1 tsp is about 5 mL; 1 tbsp is about 15 mL.
- °F to °C: subtract 32 first, then multiply by 5/9.
Swipe the picture sideways to see all of it.
On the metric ladder, each rung is a factor of 10. Kilo means 1,000 times the base unit, and milli means one-thousandth of it.
Key facts
- Metric prefixes: kilo = 1,000; hecto = 100; deka = 10; deci = 0.1; centi = 0.01; milli = 0.001; micro (µ) = 0.000001 of the base unit.
- Converting to a smaller unit gives a bigger number (0.4 g = 400 mg); converting to a bigger unit gives a smaller number (2,750 mL = 2.75 L).
- 1 inch = 2.54 cm exactly; 1 ft = 12 in; 1 mi ≈ 1.61 km.
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- 1 kg ≈ 2.2 lb, so divide pounds by 2.2 to get kilograms; 1 lb = 16 oz.
- Common health-care volume values (rounded): 1 tsp ≈ 5 mL, 1 tbsp = 3 tsp ≈ 15 mL, 1 fl oz = 2 tbsp ≈ 30 mL, 1 cup = 8 fl oz ≈ 240 mL; 1 mL = 1 cm³.
- °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32; 9/5 = 1.8.
- Dimensional analysis: multiply by unit fractions such as (1 kg / 2.2 lb) so the unwanted unit cancels; chain several fractions for multi-step conversions.
Quick check1 question · 2 more at the end
A vitamin tablet contains 0.25 g of vitamin C. How many milligrams of vitamin C does the tablet contain?
Correct answer: B.
Milli means one-thousandth, so 1 g = 1,000 mg. Converting to a smaller unit makes the number bigger: multiply by 1,000, which moves the decimal point 3 places to the right. 0.25 g × 1,000 = 250 mg.
A This moves the decimal only 1 place, as if 1 g were 10 mg.
B Correct: 0.25 × 1,000 = 250 mg, because 1 g = 1,000 mg.
C This moves the decimal only 2 places, as if 1 g were 100 mg (that would be centigrams).
D This divides by 1,000 instead of multiplying, moving the decimal the wrong way.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: Multiply by a fraction equal to 1, with the unit to cancel on the bottom. Metric prefixes change by factors of 10, so move the decimal. Know 1 kg ≈ 2.2 lb, 1 in = 2.54 cm, 1 tsp ≈ 5 mL, 1 tbsp ≈ 15 mL, 1 fl oz ≈ 30 mL, °C = (°F − 32) × 5/9.
1 How does the metric ladder work?Every step on the metric ladder is a factor of 10, so you only move the decimal point. 1 min
Every step on the metric ladder is a factor of 10, so you only move the decimal point. The base units are the meter (length), gram (mass) and liter (volume).
| Prefix | Symbol | Times the base unit |
|---|---|---|
| kilo | k | 1,000 |
| hecto | h | 100 |
| deka | da | 10 |
| (base) | m, g, L | 1 |
| deci | d | 0.1 |
| centi | c | 0.01 |
| milli | m | 0.001 |
| micro | µ | 0.000001 |
Below milli, the next prefix is three decimal places away, so 1 mg = 1,000 µg.
Worked example 1. Convert 0.4 g to milligrams, then 2,750 mL to liters.
- Grams to milligrams is 3 steps down the ladder (g, dg, cg, mg), and 1 g = 1,000 mg.
- Going down to a smaller unit, the number gets bigger: move the decimal 3 places right. 0.4 g = 400 mg.
- Milliliters to liters is 3 steps up, and 1,000 mL = 1 L.
- Going up to a bigger unit, the number gets smaller: move 3 places left. 2,750 mL = 2.75 L.
Classic wrong turn: moving the decimal the wrong way and writing 0.0004 mg. Sense check: milligrams are tiny, so you need lots of them.
2 Which US and health-care conversions should I know?A short list of conversions covers almost every health-care math problem. 1 min
A short list of conversions covers almost every health-care math problem. Tests often round to the friendly value; NIST's more precise value is shown for comparison.
| US unit | Friendly value | NIST precise value |
|---|---|---|
| 1 inch | 2.54 cm | 2.54 cm (exact) |
| 1 pound (16 oz) | 1 kg ≈ 2.2 lb | 0.4536 kg |
| 1 teaspoon (tsp) | 5 mL | 4.93 mL |
| 1 tablespoon (tbsp) = 3 tsp | 15 mL | 14.79 mL |
| 1 fluid ounce (fl oz) = 2 tbsp | 30 mL | 29.57 mL |
| 1 cup = 8 fl oz | 240 mL | 236.6 mL |
| 1 mile | 1.61 km | 1.609 km |
Also useful: 1 ft = 12 in, 1 h = 60 min, 1 L = 1,000 mL, and 1 mL = 1 cm³.
3 How do I convert between systems without guessing?Multiply by a fraction equal to 1 that puts the unit you want to cancel on the bottom. 1 min
Multiply by a fraction equal to 1 that puts the unit you want to cancel on the bottom. This is called dimensional analysis, and you can chain as many fractions as you need.
Worked example 2. How many milliliters are in 3/4 cup of broth?
- Start with what you have: 3/4 cup.
- Cancel cups: 3/4 cup × (8 fl oz / 1 cup) = 6 fl oz.
- Cancel fluid ounces: 6 fl oz × (30 mL / 1 fl oz) = 180 mL.
Classic wrong turn: using 16 fl oz per cup and getting 360 mL. Sixteen ounces is a pound, a weight; a cup is 8 fluid ounces.
The same method turns 33 lb into kilograms: 33 lb × (1 kg / 2.2 lb) = 15 kg. If your answer is 72.6 kg, you multiplied instead of divided.
4 How do I convert temperature?Temperature is the one conversion where order matters, because of the 32. 1 min
Temperature is the one conversion where order matters, because of the 32. Use °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32.
Worked example 3. Convert 38 °C to Fahrenheit.
- Multiply by 9/5 (or 1.8): 38 × 1.8 = 68.4.
- Add 32: 68.4 + 32 = 100.4 °F.
- Check by reversing: (100.4 − 32) × 5/9 = 68.4 × 5/9 = 38 °C.
Classic wrong turn: adding 32 first, (38 + 32) × 1.8 = 126 °F, which is far too hot for a body temperature.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Going from pounds to kilograms, divide by 2.2, not multiply; the kilogram number is always the smaller one.
Watch out: A cup is 8 fluid ounces; 16 ounces is a pound (weight), not a cup.
Watch out: For °F to °C, subtract 32 first and then multiply by 5/9; for °C to °F, multiply by 9/5 first and then add 32.
Watch out: Move the decimal the right way: a smaller unit needs more of them, so the number gets bigger.
Watch out: 5 ft 7 in is 67 inches, not 5.7 feet; a foot has 12 inches, not 10.
How to remember it
One habit, writing the units on every number, prevents most conversion mistakes.
Rule to remember: the unit you want to get rid of goes on the bottom of the fraction.
Memory hook: "King Henry Died By Drinking Chocolate Milk": kilo, hecto, deka, base, deci, centi, milli.
Self-check:
- Convert 1.5 L to mL and 250 mg to g.
- A child weighs 44 lb. Find the weight in kilograms.
- Convert 2 tbsp to mL, then 50 °F to °C.
Show answers
- 1,500 mL and 0.25 g.
- 1 L = 1,000 mL. Going down to a smaller unit, the number gets bigger: 1.5 × 1,000 = 1,500 mL.
- 1,000 mg = 1 g. Going up to a bigger unit, the number gets smaller: 250 ÷ 1,000 = 0.25 g.
- 20 kg.
- 44 lb × (1 kg / 2.2 lb) = 44 ÷ 2.2 = 20 kg.
- Check: the kilogram number is smaller than the pound number.
- 30 mL, then 10 °C.
- 2 tbsp × (15 mL / 1 tbsp) = 30 mL.
- Subtract 32 first: 50 − 32 = 18.
- Multiply by 5/9: 18 × 5/9 = 10 °C.