Q. 2.87 - An Introduction to General, Organic, and Biological Chemistry

Question

The length of this rug is $38.4 in$,and the width is $24.2$  in.($2.3,2.6$)

a. What is the length of this rug, in centimeters?

b. What is the width of this rug, in centimeters?

c. How many significant figures are in the length measurement?

d. Calculate the area of the rug, in square centimeters, to the correct number of significant figures, $Area=(Length\times Width)$

Step-by-Step Solution

Answer

a) The length of the rug is determined as $97.5 cm$

b) The width of the rug is determined as $61.5 cm$

c) The number of significant figures are determined as three significant figures

d) The area of the rug is calculated as $6.00\times {10}^3 c{m}^2$

Step 1 : Introduction (part a)

The given is the picture of a rug with certain measurements

The objective is to determine the length, width, significant figures and the area of the rug

Step 1 : Explanation (part a)

a.

To obtain the result in centimeters, use the following equality between inches and centimeters and extract the appropriate conversion factor.

$1 in=2.54 cm$

The following are the conversion factors:

$\frac{1\mathrm{in}.}{2.54 \mathrm{cm}}$ and $\frac{2.54 \mathrm{cm}}{1\mathrm{in}.}$

The conversion factor that should be used is as follows:

$\frac{2.54 \mathrm{cm}}{1\mathrm{in}.}$

Determine the length in centimeters from the desired conversion factor. $38.4\mathrm{in}$.

$38.4 in \times 2.54 cm1 in=97.5 cm$

Thus, the length of the rug will be $97.5 \mathrm{cm}$.

Step 3 : Introduction (part b)

The objective is to determine the length, width, significant figures and the area of the rug

Step 4: Explanation (part b)

b.

Use the conversion factor you want. $\frac{2.54 \mathrm{cm}}{1\text{ in. }}$ to calculate the width in millimetres $24.2 in$ .

$$\begin{gathered} 24.2 in \times \frac{2.54 cm}{1 in}. \\ =61.5 cm \end{gathered}$$

Thus, the width of the rug will be $61.5 \mathrm{cm}$.

The rug's length is $38.4 in. (97.5 cm)$ 

Step 5 : Introduction (part c)

The objective is to determine the length, width, significant figures and the area of the rug

Step 6 : Explanation (part c)

c.

Because all nonzero digits are significant has three significant figures.

Step 7 : Introduction (part d)

The objective is to determine the length, width, significant figures and the area of the rug

Step 8 : Explanation (part d)

d.

The area is calculated by multiplying the length by the width.

$Area =length \times width$

$=97.5 \mathrm{cm}\times 61.5 \mathrm{cm}$

$=6.00\times {10}^3{ \mathrm{cm}}^2$ (up to 3 significant figures)

So, the area of rug will be $6.00\times {10}^3{ \mathrm{cm}}^2$