To convert currency, use the exchange rate as a multiplier in one direction and a divisor in the other. The rate tells you how many units of one currency equal one unit of another, and the skill is choosing the correct direction.
This is the first skill in international trade and exchange rates. It supports every later lesson, because appreciation, depreciation and the effects on traders all start from a converted price.
What does an exchange rate actually say?
An exchange rate is the price of one currency in terms of another. Take two fictional economies. Doravia uses the dora and Kesland uses the kesa. Suppose the quoted rate is:
1 dora = 5 kesa
Read it like a price tag. One dora costs 5 kesa, so a dora is worth more than a kesa. That tells you something useful before you calculate: the same amount of money will be a bigger number in kesa than in dora.
How do I convert in either direction?
- Write the rate as a sentence, with the currency you are given on one side.
- Decide the direction. To move from dora to kesa, each dora becomes 5 kesa, so multiply by 5.
- For kesa to dora, divide by 5, because 5 kesa make one dora.
- Sense-check. Dora is the stronger unit here, so the dora amount must be the smaller number.
Worked example
A café in Kesland buys a coffee machine from a Doravian firm. The price is 2,400 dora. The rate is 1 dora = 5 kesa. How much does the café pay in kesa?
Step 1, sentence: 1 dora = 5 kesa.
Step 2, direction: dora to kesa, so multiply.
Step 3, calculate: 2,400 × 5 = 12,000.
Answer: 12,000 kesa.
Sense-check: kesa is the weaker currency, so the kesa figure should be larger than 2,400. It is.
Now reverse it. A Kesland visitor returns home with 750 kesa left over and wants to change it back to dora. Divide: 750 ÷ 5 = 150 dora.
The mistake to watch for
The usual slip is multiplying every time because “convert” sounds like multiplication.
Mistaken answer: 750 kesa × 5 = 3,750 dora.
The student multiplied when going from the weaker currency to the stronger one.
The correction is the sense-check. 750 kesa cannot turn into 3,750 dora, because a dora is worth 5 kesa, so the dora figure must be smaller than 750. Dividing gives 150, which passes the check.
Check yourself
Use 1 dora = 5 kesa for all three questions.
1. A Doravian student buys a book that costs 80 dora. What is that in kesa?
Show answer
Dora to kesa, so multiply: 80 × 5 = 400 kesa.
2. A Kesland shop receives 1,350 kesa from a Doravian customer. What is that in dora?
Show answer
Kesa to dora, so divide: 1,350 ÷ 5 = 270 dora.
3. A Kesland family books 3 hotel nights in Doravia at 120 dora per night. What is the total in kesa?
Show answer
Total in dora: 3 × 120 = 360. Convert: 360 × 5 = 1,800 kesa.
Where this leads next
Once conversion is automatic, move on to telling appreciation from depreciation, where the rate itself changes and you compare two conversions. The percentage-base explorer helps you practise the percentage steps that follow.
Some students can convert one price but lose track in a longer question with two currencies and a change in the rate. A teacher on our online one-to-one Economics tuition can work through that kind of question with you at your own pace.