Q. 2.99 - An Introduction to General, Organic, and Biological Chemistry

Question

In France, grapes are $2.20 \mathrm{lb}$ per kilogram. What is the cost of grapes, in dollars per pound, if the exchange rate is $1.14 \text{dollars/euro}$. 

Step-by-Step Solution

Answer

After rounding off the three significant figures, the cost of grapes is calculated as $1.08 \$ \text{per pound}$

Part (a) Step 1: Given Information

The given is the cost of grapes in France per kilogram

The objective is to find the cost of the grapes after rounding off to three significant figures

Part (a) Step 2: Explanation

The cost of grapes is,

cost of grapes $=1.95$ Euros $/\mathrm{kg}$

So, the cost of gapes is,

cost of grapes $=1.95$ Euros per $2.20\mathrm{lb}$

Cost per pound is,

$\text{ cost per pound }=1.95\text{ Euros }/\mathrm{kg}\left(\frac{1 \mathrm{kg}}{2.20\mathrm{lb}}\right)$

$=0.88636$$\text{ Euro }/\mathrm{lb}$

The values $\$1.95$ and $2.20$ have three significant figures.

Part (b) Step 1: Given Information

The given is the cost of grapes in France per kilogram

The objective is to find the cost of the grapes after rounding off to three significant figures 

Part (b) Step 2: Explanation

Cost of grapes $=1.75 \mathrm{Euros} / \mathrm{kg}$

AS

$1 \mathrm{kg}=2.20\mathrm{lb}$

So the cost of grapes $=1.75 \text{Euros per} 2.20\text{ lb}$

Cost per pound

$\frac{1.75}{2.20}=0.7954$. Euro / pound

$1.75$ and $2.20$ have three significant features So, if you round up to three significant figures, you get$0.795$ Euros per pound.

Given is 1 Euro $=1.36$

So $0.795$ Euros per pound $=0.795\times 1.36$ per pound $=1.0812 \mathrm{S}$ per pound

Since $0.795\&1.36$ have three significant features So, if you round up to three significant figures, gives $\$1.08$per pound.