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 Grams

A bag of rice weighs $2.5$ kg. How many grams is this?

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

Apply the conversion: $2.5 \times 1000$ = $2500$

Add the unit: $2500$ g = Answer in grams

Answer: $2.5$ kg $= 2500$ g

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: Confusing mass and weight in contexts

Why: In everyday language, we use these interchangeably, but mass is measured in grams/kg.

Correct: On Earth, mass and weight are proportional. Use metric units (g, kg) for mass measurements.

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 is there no 'hectogram' or 'dekagram' commonly used?

A: While these units exist (100 g and 10 g), they are rarely used in everyday life. We typically jump from grams to kilograms because the factor of 1000 is convenient.

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.