Money Conversions

An exchange rate links two currencies. The way it's written matters:

"$1 = £0.78" means: $1 converts to £0.78.

To convert from $ to £, MULTIPLY by $0.78$:

$245 → $245 \times 0.78 = 191.10$, so £191.10.

To convert the other way (£ to $), DIVIDE by $0.78$ (or multiply by $1/0.78 \approx 1.282$):

£100 → $100 \div 0.78 = 128.21$, so $128.21.

Quick test of direction. If you ended up with $1{,}000{,}000$ when converting a holiday spending amount, you went the wrong way. Sanity-check the magnitude.

Round to currency precision. Most currencies round to 2 d.p. (cents, pence, centimes). Some — JPY, KRW — use 0 d.p. (whole units). Cambridge usually states the rounding requirement.

If the question gives "$1 = £0.78" and "$1 = €0.92", but you need "£ to €":

1. Convert £ to $: divide by $0.78$.
2. Convert $ to €: multiply by $0.92$.

Combined: the £ → € rate is $\dfrac{0.92}{0.78} \approx 1.179$. So £100 = €117.95.

Worked. Convert £250 to euros, given the two rates above.

• Method 1 (step-by-step): $250 / 0.78 = 320.51$, so $320.51. Then $320.51 \times 0.92 = 294.87$, so €294.87.
• Method 2 (combined rate): $250 \times 1.179 = 294.87$, so €294.87.

Same answer, fewer keystrokes if you spot the combined rate first.

Sales tax / VAT. A percentage ADDED to the pre-tax price.

Worked. "An item costs $80 before $7\%$ tax." Final price = $80 \times 1.07 = 85.60$, so $85.60.

To recover the pre-tax price from the post-tax: divide by the multiplier. $85.60 / 1.07 = 80$, so $80.

Commission on currency exchange. Bureaux de change charge a percentage commission. Cambridge can phrase it two ways:

1. Commission deducted from the amount. If you exchange $100 at $1\%$ commission, only $99 is converted.
2. Commission charged on top. If $100 is converted and the bureau charges $1\%$, the customer hands over $101.

Read carefully — examiners deliberately pick one phrasing.

Worked. "Convert $500 to £ at $1 = £0.78, with $2\%$ commission deducted from the dollars before conversion."

1. Commission: $500 \times 0.02 = 10$, so $10.
2. Amount actually converted: $500 - 10 = 490$, so $490.
3. £ received: $490 \times 0.78 = 382.20$, so £382.20.

Most currency answers should be rounded to 2 decimal places, regardless of any "3 s.f." instruction the question gives elsewhere. Banking convention rounds half-up.

$, £, € — 2 decimal places. $12.7384 → $12.74.

¥ (Japanese yen) — 0 decimal places. ¥$1245.6$ → ¥$1246$.

Some currencies (KWD Kuwaiti dinar) use 3 decimal places. Cambridge specifies if so.

Always specify the currency symbol. "$80$" is meaningless; "$80" is correct.

Multi-step calculations. Carry full precision until the FINAL answer; round only once at the end. Rounding intermediate steps compounds errors.