Converting Grams to Milligrams

A tablet contains $0.5$ g of medicine. How many milligrams is this?

Identify the conversion: $1$ g $= 1000$ mg = Multiply by 1000

Apply the conversion: $0.5 \times 1000$ = $500$

Add the unit: $500$ mg = Answer in milligrams

Answer: $0.5$ g $= 500$ mg

Converting Kilograms to Tonnes

A hippopotamus has a mass of $1800$ kg. What is its mass in tonnes?

Identify the conversion: $1$ t $= 1000$ kg = Divide by 1000

Apply the conversion: $1800 \div 1000$ = $1.8$

Add the unit: $1.8$ t = Answer in tonnes

Answer: $1800$ kg $= 1.8$ t

Converting Tonnes to Kilograms

A small car weighs $1.2$ tonnes. What is its mass in kilograms?

Identify the conversion: $1$ t $= 1000$ kg = Multiply by 1000

Apply the conversion: $1.2 \times 1000$ = $1200$

Add the unit: $1200$ kg = Answer in kilograms

Answer: $1.2$ t $= 1200$ kg

Multi-Step Conversion

Convert $3{,}500{,}000$ mg to kilograms.

Plan the conversion path: mg → g → kg = Two steps needed

Convert mg to g: $3{,}500{,}000 \div 1000 = 3500$ g = Divide by 1000

Convert g to kg: $3500 \div 1000 = 3.5$ kg = Divide by 1000 again

Verify (optional): $3{,}500{,}000 \div 1{,}000{,}000 = 3.5$ kg = Direct conversion confirms

Answer: $3{,}500{,}000$ mg $= 3.5$ kg

Mistake: Multiplying when you should divide (or vice versa)

Why: Going from a smaller unit to a larger unit means you have fewer of them, so you divide.

Correct: Smaller to larger unit = divide. Larger to smaller unit = multiply. Example: g to kg = divide by 1000.

Mistake: Forgetting that 1 tonne = 1,000,000 grams

Why: Students often only remember kg to g conversion and forget the tonne relationship.

Correct: $1$ t $= 1000$ kg, and $1000 \times 1000 = 1{,}000{,}000$ g

Mistake: Moving the decimal point the wrong number of places

Why: Between mg, g, kg and t the factor is always 1000, so the decimal point moves 3 places, not 1 or 2. A typical slip is writing 2.5 kg = 250 g.

Correct: $2.5$ kg $= 2.5 \times 1000 = 2500$ g: move the decimal point 3 places to the right.

Medicine and Supplements

Medicine doses are often measured in milligrams because the amounts are very small.

A pain reliever tablet might contain $500$ mg of the active ingredient. That is only $0.5$ g!

Cooking and Recipes

Recipes use grams for precise measurements, especially in baking.

A cake recipe needs $250$ g of flour, $200$ g of sugar, and $125$ g of butter.

Shipping and Transport

Heavy loads are measured in tonnes because kilograms would give very large numbers.

A shipping container might weigh $25$ tonnes. That is $25{,}000$ kg or $25{,}000{,}000$ g!

Q: What is the difference between mass and weight?

A: Mass is the amount of matter in an object and is measured in grams or kilograms. Weight is the force of gravity on that mass. On Earth, they are proportional, so we often use them interchangeably.

Q: Why are the hectogram and the decagram rarely used?

A: These units exist (1 hg = 100 g, 1 dag = 10 g), but most people go straight from grams to kilograms. There are exceptions: in Italy you buy ham by the 'etto' (100 g), in the Netherlands an 'ons' means 100 g, and in Austria shops sell by the 'Deka' (10 g).

Q: Is a metric tonne the same as a US ton?

A: No! A metric tonne (t) is $1000$ kg. A US ton (short ton) is about $907$ kg. Always check which unit is being used.