Q. 2.48 - 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 liter is $1.06 qt$

b. At the store, oranges are $\$1.29$per $lb$

c. One deciliter contains $100 mL$

d. An $18$ -carat gold ring contains $75\%$ gold by mass.

Step-by-Step Solution

Answer

The equality and conversion factors are:

(a) $1 L=1.06 qt;\frac{1 L}{1.06 qt} , \frac{1.06 qt}{1 L} ;$$1.06 qt$has $3$ significant figures and $1 L$ is exact.

(b)$\$1.29 = 1 lb$ orange; $\frac{\$1.29}{1 lb orange} ,\frac{1 lb orange}{\$1.29}$;$\$1.29$has $3$ significant figure and $1 lb$ is exact.

(c)$1 dL = 100 mL; \frac{100 mL}{1 dL}, \frac{1 dL}{100 mL};$ $100 mL$ has $3$significant figures and $1 dL$ is exact.

(d) $$\begin{gathered} 100 g(18 carat gold)=75g(pure gold); \frac{75g(pure gold)}{100 g(18 carat gold)} \\ ,\frac{100 g(18 carat gold)}{75g(pure gold)} \end{gathered}$$

$100 g$has $1$ significant figure and $75 g$ has $2$ significant figures

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 : One liter is $1.06 qt$.

Part(a) Step 2:Explanation

Equality	Conversion Factors	Significant figures or exact
$1 liter = 1.06 qt$	$$\begin{gathered} \frac{1.06 qt}{1 liter} \\ \frac{1 liter}{1.06 qt} \end{gathered}$$	$1.06 qt$is measured. It has $2$ significant figures. $1 liter$ is 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: Oranges are $ $1.29 per lb$

Part(b) Step 2:Explanation

Equality	Conversion Factors	Significant figures or Exact
$1 lb$ orange = $\$1.29$	$$\begin{gathered} \frac{1 lb orange}{\$1.29} \\ \frac{\$1.29}{1 lb orange} \end{gathered}$$	$\$1.29$has $3$ significant figures and $1 lb$ 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: One deciliter contains $100 mL$.

Part(c) Step 2:Explanation

Equality	Conversion Factors	Significant figures or Exact
$1 dL = 100 mL$	$$\begin{gathered} \frac{1 dL}{100 mL} \\ \frac{100 mL}{1 dL} \end{gathered}$$	$100 mL$has one significant figure.$1 dL$ 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 : $18$ -carat gold ring contains $75 \%$ gold by mass.

Part(d) Step 2:Explanation

Equality	Conversion Factors	Significant figures or Exact
$100 g$($18$ carat gold) = $75 g$(pure gold)	$$\begin{gathered} \frac{100 g(18 carat gold)}{75 g(pure gold)} \\ \frac{75 g(pure gold)}{100 g(18 carat gold)} \end{gathered}$$	$100 g$has three significant figures. $75 g$has 2 significant figures.