Unit Conversions

Unit conversion questions appear regularly in the UCAT QR subtest. The conversions themselves are straightforward — the challenge is performing them quickly and accurately under time pressure. This lesson covers the metric conversions, time conversions, and compound unit conversions that appear most often.

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Metric Length Conversions

Conversion	Factor	Direction
km → m	×1,000	Larger to smaller: multiply
m → cm	×100	Larger to smaller: multiply
cm → mm	×10	Larger to smaller: multiply
m → km	÷1,000	Smaller to larger: divide
cm → m	÷100	Smaller to larger: divide
mm → cm	÷10	Smaller to larger: divide

The Golden Rule: Converting from a larger unit to a smaller unit → multiply (you need more of the smaller units). Converting from a smaller unit to a larger unit → divide.

Quick Reference Chain

km → m → cm → mm

Each step: ×10, ×100, or ×1,000 depending on how many steps.

• 2.5 km = 2,500 m = 250,000 cm = 2,500,000 mm
• 45 mm = 4.5 cm = 0.045 m = 0.000045 km

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Metric Mass Conversions

Conversion	Factor
kg → g	×1,000
g → mg	×1,000
g → kg	÷1,000
mg → g	÷1,000
tonnes → kg	×1,000

Common QR Scenarios

• Nutritional information (grams, milligrams per serving)
• Medication dosages (mg per tablet, total mg needed)
• Recipe scaling (grams of ingredients)

Example: A tablet contains 250 mg of a drug. A patient needs 1.5 g per day. How many tablets?

• 1.5 g = 1,500 mg
• 1,500 ÷ 250 = 6 tablets

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Metric Volume/Capacity Conversions

Conversion	Factor
litres → ml	×1,000
ml → litres	÷1,000
m³ → litres	×1,000
cm³ → ml	×1 (they are equal)

Key fact: 1 cm³ = 1 ml. This is used frequently in scientific data questions.

Example: A container holds 2.4 litres. How many 150 ml cups can be filled?

• 2.4 litres = 2,400 ml
• 2,400 ÷ 150 = 16 cups

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Time Conversions

Time conversions cause more errors than any other type in QR, because time does not follow the decimal system.

Conversion	Factor
hours → minutes	×60
minutes → seconds	×60
hours → seconds	×3,600
days → hours	×24
weeks → days	×7

The "0.5 Hours ≠ 50 Minutes" Trap

• 0.5 hours = 30 minutes (not 50)
• 0.75 hours = 45 minutes (not 75)
• 0.1 hours = 6 minutes (not 10)
• 1.5 hours = 90 minutes (not 150)

Converting Decimal Hours to Hours and Minutes

Method: Multiply the decimal part by 60.

Decimal Hours	Hours	Minutes (decimal × 60)	Result
2.25	2	0.25 × 60 = 15	2 hours 15 min
3.75	3	0.75 × 60 = 45	3 hours 45 min
1.4	1	0.4 × 60 = 24	1 hour 24 min
0.8	0	0.8 × 60 = 48	48 minutes

Converting Minutes to Decimal Hours

Method: Divide the minutes by 60.

Time	Calculation	Decimal Hours
2 hours 30 min	2 + 30/60	2.5
1 hour 45 min	1 + 45/60	1.75
3 hours 20 min	3 + 20/60	3.333...

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Speed, Distance, and Time Conversions

The Formula Triangle

To Find	Formula
Distance	Speed × Time
Speed	Distance ÷ Time
Time	Distance ÷ Speed

Converting Speed Units

Conversion	Method
km/h → m/s	÷3.6 (or ×1,000 ÷3,600)
m/s → km/h	×3.6
mph → km/h	×1.6 (approximate)
km/h → mph	÷1.6 (approximate)