Q.2.88 - An Introduction to General, Organic, and Biological Chemistry

Question

A shipping box has a length of 7.00 in., a width of 6.00 in., and a height of 4.00 in. (2.3,2.6)

a. What is the length of the box, in centimeters?

b. What is the width of the box, in centimeters?

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

d. Calculate the volume of the box, in cubic centimeters, to the correct number of significant figures.

Step-by-Step Solution

Answer

Part (a). $17.8$cm

Part (b). $15.2$cm

Part (c). $3$ cm

Part (d). $2.75\times {10}^3$${\mathrm{cm}}^3$

Part (a) Step 1: General information

Significant figures of a number in positional documentation are digits in the number that are solid and important to demonstrate the amount of something.

Part (a) Step 2: explanation

We know 

$1$ inch = $2.54 \mathrm{cm}$

hence,

 $$\begin{gathered} 7 \mathrm{in}=7\times 2.54 \mathrm{cm} \\ =17.8 \mathrm{cm} \end{gathered}$$

Part (b) Step 3: explanation

We know 

1 inch = $2.54 \mathrm{cm}$

hence,

$$\begin{gathered} 6 \mathrm{in}=6\times 2.54 \\ =15.2 \mathrm{cm} \end{gathered}$$

Part (c) Step 4: explanation

Significant figures in the width measurement are = $3$

Part (d) Step 5: explanation

The volume is,

$\mathrm{l}\times \mathrm{b}\times \mathrm{h}$

$$\begin{gathered} =17.8\times 15.2\times 10.16 \\ =2.74\times {10}^3 {\mathrm{cm}}^3 \end{gathered}$$