Basic Conversions
Basic conversions change measurements from one unit to another within the same system, such as converting metres to centimetres or grams to kilograms. The metric system uses factors of 10, 100, and 1000 to relate different units. Converting to smaller units requires multiplication, while converting to larger units requires division.
Why it matters
Basic conversions appear throughout daily life in the UK, from calculating fuel efficiency (miles per gallon to kilometres per litre), understanding weather reports (Celsius temperatures), and managing household measurements for cooking and DIY projects. A recipe calling for 250 mL of milk requires converting if measuring cups show litres. Pharmacists convert between milligrams and grams for dosages, whilst engineers convert millimetres to metres for construction plans. In GCSE mathematics, conversion skills underpin area calculations (square centimetres to square metres), volume problems, and scientific notation. These foundations support advanced topics like dimensional analysis in A-level physics and chemistry, where students might convert between joules per kilogram and calories per gram.
How to solve basic conversions
Basic Unit Conversions
- To convert to a smaller unit: multiply (e.g. m → cm: ×100).
- To convert to a larger unit: divide (e.g. g → kg: ÷1000).
- Key: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL.
- Line up units before converting.
Example: 3.5 km = 3.5 × 1000 = 3500 m.
Worked examples
How many mL in 1 L?
Answer: 1000
- Remember the conversion factor → 1 L = 1000 mL — A big bottle of water is 1 litre. That's 1000 mL. A teaspoon holds about 5 mL, so 200 teaspoons fill a litre.
- Think about why it works → 1000 mL fit inside 1 L — The prefix tells you: 'kilo' means 1000, 'centi' means 1/100, 'milli' means 1/1000. So 1 L always equals 1000 mL.
- State the answer → 1000 — There are 1000 mL in 1 L.
How many m are in 2 km?
Answer: 2000
- Remember: 1 km = 1000 m → 1 km = 1000 m — This is our conversion factor. We're going from a bigger unit (km) to a smaller unit (m), so each km contains 1000 m.
- Going from bigger to smaller means MULTIPLY → 2 x 1000 = ? — When you break a big unit into smaller pieces, you get MORE pieces. Think of breaking a chocolate bar into squares -- you end up with more squares than bars. So we multiply.
- Calculate → 2 x 1000 = 2000 m — So 2 km = 2000 m. Each of the 2 km contributes 1000 m.
How many m is 675 cm?
Answer: 6.75
- Remember: 1 m = 100 cm → 1 m = 100 cm — We need to convert from cm (smaller unit) to m (bigger unit). Each m contains 100 cm.
- Going from smaller to bigger means DIVIDE → 675100 = ? — When you group small units into bigger bundles, you get FEWER bundles. Think of putting 1000 gummy bears into bags of 1000 -- you'd have fewer bags than bears. So we divide.
- Calculate → 675100 = 6.75 m — 675 cm = 6.75 m. You can check: 6.75 x 100 = 675.
Common mistakes
- Multiplying when dividing is needed produces incorrect results, such as converting 500 cm to metres as 500 × 100 = 50,000 m instead of 500 ÷ 100 = 5 m
- Confusing conversion factors leads to errors like treating 1 km as 100 m instead of 1000 m, giving 3 km = 300 m rather than 3000 m
- Mixing up decimal placement when converting produces answers like 2.5 L = 25 mL instead of 2500 mL