Q. 2.47 - An Introduction to General, Organic, and Biological Chemistry

Question

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following:

a. One yard is $3 ft.$

b. One kilogram is $2.20 lb$

c. A car goes $27 mi$ on $1 gal$ of gas .

d. Sterling silver is $93\%$ silver by mass.

Step-by-Step Solution

Answer

The equality and conversion factors are:

(a)  $1 yd = 3 ft$; $\frac{3 ft}{1 yd}$ and $\frac{1 yd}{3 ft}$; Both $1 yd$ and $3 ft$ are exact.

(b) $1 kg = 2.20 lb$; $\frac{2.20 lbs}{1 kg}$ and $\frac{1 kg}{2.20 lbs}$;$2.20 lbs$ is measured and has $3$SF's and $1 kg$ is Exact

(c) $1 gal = 27 mi$ ; $\frac{1 gal}{27 mi}$and $\frac{27 mi}{1 gal}$; $27$ is measures and has $2$SF's and $1 gal$ is exact.

(d) $93 g$ of silver = $100 g$ sterling ;$\frac{93 g}{100 g}$ and $\frac{100 g}{93 g}$; $93 g$ is measured and has $2$SF's and $100 g$ is exact.

Part(a) Step 1: Given Information

We need to find the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for $1 yard$ is $3 ft.$

Part(a) Step 2: Explanation

Equality	Conversion Factor	Significant figures or exact
$1 yard = 3 ft$	$$\begin{gathered} \frac{1 yard}{3 ft.} \\ \frac{3 ft.}{1 yard} \end{gathered}$$	Both $1 yard$ and $3 ft.$ are exact

Part(b) Step 1: Given Information

We need to find the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for $1 kg$ is $2.20 lb$

Part(b) Step 2: Explanation

Equality	Conversion Factor	Significant figures and exact
$1 Kg = 2.20 lb$	$$\begin{gathered} \frac{1 kg}{2.20 lb} \\ \frac{2.20 lb}{1 kg} \end{gathered}$$	$2.20 lbs$ is measured and has 3 significant figure. $1 kg$is exact.

Part(c) Step 1: Given Information

We need to find the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for A car goes $27 mi$ on $1 gal$ of gas

Part(c) Step 2: Explanation

Equality	Conversion Factor	Significant Figures and Exact
$1 gal = 27 mi$	$$\begin{gathered} \frac{1 gal}{27 mi} \\ \frac{27 mi}{1 gal} \end{gathered}$$	$27$ has two significant figures and $1 gal$ is exact.

Part(d) Step 1: Given Information

We need to find the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures in Sterling silver is $93 \%$ silver by mass

Part(d) Step 2: Explanation

Equality	Conversion Factor	Significant Figures and Exact
$93 g$of silver =$100 g$sterling	$$\begin{gathered} \frac{93 g}{100g} \\ \frac{100 g}{93 g} \end{gathered}$$	$93 g$has $2$ significant figures and $100 g$is exact.