GCSE Maths Practice: currency-conversion

Higher GCSE Currency Conversion with Three-Decimal Exchange Rates

At Higher GCSE level, currency conversion questions often include exchange rates with three decimal places. These are used to test precision, accurate decimal multiplication, and sensible rounding. Multiple-choice formats add an additional challenge, as students must judge which answers are reasonable before confirming the correct one with calculation.

Understanding the Exchange Rate

An exchange rate such as £1 = €1.235 means that every pound is worth one euro and 23.5 cents. Because the exchange rate is greater than 1, converting from pounds to euros will increase the numerical value. Recognising this immediately allows you to eliminate options that are clearly too small.

Three-decimal exchange rates are common at Higher tier because they require careful handling of decimal places and discourage over-rounding.

Using Estimation Effectively

Before calculating exactly, it is helpful to estimate the answer. Rounding €1.235 to €1.24 or even €1.20 can give you a quick sense of scale. For example, converting £250 at approximately €1.20 per pound would give an answer just above €300. This immediately removes options far from that value.

Exact Calculation Method

Once you have estimated, confirm the answer by calculating accurately:

• Write down the multiplication clearly.
• Multiply using full decimal precision.
• Keep all decimal places during the calculation.
• Round only the final answer to two decimal places.

Rounding too early is one of the most common Higher-tier mistakes.

Worked Example (Different Numbers)

Suppose the exchange rate is £1 = €1.247.

Convert £180 to euros.

Step 1: Estimate first. £180 × 1.25 ≈ €225, so the answer should be slightly lower.

Step 2: Multiply: 180 × 1.247 = 224.46

Step 3: Write the final amount → €224.46

Another Example

If £1 = €1.198 and someone exchanges £415:

415 × 1.198 = 497.17 → €497.17

Common Higher-Tier Errors

• Misplacing decimal points: Always count decimal places carefully.
• Choosing a rounded-looking option: Correct answers are often not neat numbers.
• Skipping estimation: Estimation helps eliminate unreasonable options quickly.
• Rounding mid-calculation: This reduces accuracy.

Real-Life Context

Accurate currency conversion using precise exchange rates is important in real life, such as:

• Paying for international travel or accommodation
• Converting large online purchases
• Understanding bank and foreign exchange rates
• Managing overseas business transactions

Frequently Asked Questions

Why do Higher GCSE questions use three-decimal rates?
They test precision, careful calculation, and rounding discipline.

Is estimation enough in multiple-choice questions?
Estimation helps narrow choices, but calculation should confirm the answer.

Should I always give two decimal places?
Yes. Money values should normally be written to two decimal places.

Study Tip

For Higher-tier multiple-choice currency questions, estimate first to remove impossible answers, then calculate carefully and round only once at the end.