GCSE Maths Practice: currency-conversion

Higher GCSE Currency Conversion with Three-Decimal Exchange Rates

At Higher GCSE level, currency conversion questions are designed to test careful decimal multiplication, correct interpretation of exchange rates, and accurate rounding. Exchange rates with three decimal places are particularly effective at revealing small calculation errors, which is why they are commonly used in Higher-tier exams.

Understanding the Exchange Rate

An exchange rate such as £1 = €1.305 means that one pound is worth one euro and 30.5 cents. Because the exchange rate is greater than 1, converting from pounds to euros will increase the numerical value of the amount. Recognising this before calculating helps you judge whether your final answer is sensible.

Before starting the calculation, it is helpful to estimate. Rounding €1.305 to €1.30 gives a quick approximation. Multiplying £195 by €1.30 would give €253.50, so the correct answer should be slightly higher than this estimate.

Correct Method for Higher Tier Questions

To avoid errors, use a clear and structured method:

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

Rounding during intermediate steps is one of the most common reasons students lose marks on Higher-tier currency questions.

Worked Example (Different Numbers)

Suppose the exchange rate is £1 = €1.312.

Convert £168 to euros.

Step 1: Estimate first. £170 × 1.3 ≈ €221, so the answer should be close to this.

Step 2: Multiply: 168 × 1.312 = 220.416

Step 3: Round to two decimal places → €220.42

Another Example

If £1 = €1.287 and someone exchanges £245:

245 × 1.287 = 315.315 → €315.32

Common Higher-Tier Errors

• Misplacing decimal points: Always count decimal places carefully.
• Rounding too early: This reduces accuracy.
• Ignoring estimation: Estimation helps catch large mistakes.
• Assuming answers will be neat: Correct answers are often awkward decimals.

Real-Life Applications

Accurate currency conversion is essential in many real-world situations, including:

• Online shopping from overseas retailers
• Paying for travel or accommodation abroad
• Managing international expenses
• Understanding bank and exchange bureau calculations

Frequently Asked Questions

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

Should I always estimate first?
Yes. Estimation helps you judge whether your final answer is reasonable.

Do I always round to two decimal places?
Yes, because currency values are normally written to two decimal places.

Study Tip

For Higher GCSE currency conversion, always estimate first, calculate using full precision, and round only once at the end. This habit greatly reduces errors.