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 $1.06qt$

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

c. One deciliter contains $100mL$

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

Short answer

The equality and conversion factors are:

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

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

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

(d)role="math" localid="1651809879256" $$\begin{gathered} 100g(18caratgold)=75g(puregold);\frac{75g(puregold)}{100g(18caratgold)} \\ ,\frac{100g(18caratgold)}{75g(puregold)} \end{gathered}$$

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

Step-by-step solution

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 $1.06qt$.

Part(a) Step 2:Explanation

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

Part(b) Step 2:Explanation

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

Part(c) Step 2:Explanation

Equality	Conversion Factors	Significant figures or Exact
$1dL=100mL$	$$\begin{gathered} \frac{1dL}{100mL} \\ \frac{100mL}{1dL} \end{gathered}$$	$100mL$has one significant figure.$1dL$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
$100g$($18$carat gold) =$75g$(pure gold)	$$\begin{gathered} \frac{100g(18caratgold)}{75g(puregold)} \\ \frac{75g(puregold)}{100g(18caratgold)} \end{gathered}$$	$100g$has three significant figures. $75g$has 2 significant figures.