Question

complete the following table. round each of your answers to 3 significant digits.

food	energy content when eaten
a chocolate chip cookie	$4.50 \times 10^4$	$\square$	$\square$
a 12-ounce soft drink	$\square$	150.	$\square$
a baked potato	$\square$	$\square$	920.

Explanation:

To solve this, we use the energy conversion factors: \(1\ \text{kcal} = 1000\ \text{cal}\) and \(1\ \text{kcal} = 4.184\ \text{kJ}\) (or \(1\ \text{cal} = 4.184\ \text{J}\)). We'll process each food item:

1. Chocolate Chip Cookie

• Cal to kcal: \(1\ \text{kcal} = 1000\ \text{cal}\), so \(4.50 \times 10^4\ \text{cal} = \frac{4.50 \times 10^4}{1000} = 45.0\ \text{kcal}\).
• kcal to kJ: \(1\ \text{kcal} = 4.184\ \text{kJ}\), so \(45.0\ \text{kcal} \times 4.184\ \text{kJ/kcal} \approx 188\ \text{kJ}\) (3 sig figs).

2. 12 - Ounce Soft Drink

• kcal to cal: \(150\ \text{kcal} = 150 \times 1000 = 1.50 \times 10^5\ \text{cal}\).
• kcal to kJ: \(150\ \text{kcal} \times 4.184\ \text{kJ/kcal} \approx 628\ \text{kJ}\) (3 sig figs).

3. Baked Potato

• kJ to kcal: \(920\ \text{kJ} = \frac{920}{4.184} \approx 220.\ \text{kcal}\) (3 sig figs, the decimal shows precision).
• kcal to cal: \(220.\ \text{kcal} = 220. \times 1000 = 2.20 \times 10^5\ \text{cal}\).

Filled Table (Rounded to 3 Sig Figs):

Food	cal	kcal	kJ
12 - Ounce Soft Drink	\(1.50 \times 10^5\)	\(150.\)	\(628\)
Baked Potato	\(2.20 \times 10^5\)	\(220.\)	\(920.\)

Final Answers (Filled in the Table):

• Chocolate Chip Cookie:
• kcal: \(\boldsymbol{45.0}\)
• kJ: \(\boldsymbol{188}\)
• 12 - Ounce Soft Drink:
• cal: \(\boldsymbol{1.50 \times 10^5}\)
• kJ: \(\boldsymbol{628}\)
• Baked Potato:
• cal: \(\boldsymbol{2.20 \times 10^5}\)
• kcal: \(\boldsymbol{220.}\)

Answer:

To solve this, we use the energy conversion factors: \(1\ \text{kcal} = 1000\ \text{cal}\) and \(1\ \text{kcal} = 4.184\ \text{kJ}\) (or \(1\ \text{cal} = 4.184\ \text{J}\)). We'll process each food item:

1. Chocolate Chip Cookie

• Cal to kcal: \(1\ \text{kcal} = 1000\ \text{cal}\), so \(4.50 \times 10^4\ \text{cal} = \frac{4.50 \times 10^4}{1000} = 45.0\ \text{kcal}\).
• kcal to kJ: \(1\ \text{kcal} = 4.184\ \text{kJ}\), so \(45.0\ \text{kcal} \times 4.184\ \text{kJ/kcal} \approx 188\ \text{kJ}\) (3 sig figs).

2. 12 - Ounce Soft Drink

• kcal to cal: \(150\ \text{kcal} = 150 \times 1000 = 1.50 \times 10^5\ \text{cal}\).
• kcal to kJ: \(150\ \text{kcal} \times 4.184\ \text{kJ/kcal} \approx 628\ \text{kJ}\) (3 sig figs).

3. Baked Potato

• kJ to kcal: \(920\ \text{kJ} = \frac{920}{4.184} \approx 220.\ \text{kcal}\) (3 sig figs, the decimal shows precision).
• kcal to cal: \(220.\ \text{kcal} = 220. \times 1000 = 2.20 \times 10^5\ \text{cal}\).

Filled Table (Rounded to 3 Sig Figs):

Food	cal	kcal	kJ
12 - Ounce Soft Drink	\(1.50 \times 10^5\)	\(150.\)	\(628\)
Baked Potato	\(2.20 \times 10^5\)	\(220.\)	\(920.\)

Final Answers (Filled in the Table):

• Chocolate Chip Cookie:
• kcal: \(\boldsymbol{45.0}\)
• kJ: \(\boldsymbol{188}\)
• 12 - Ounce Soft Drink:
• cal: \(\boldsymbol{1.50 \times 10^5}\)
• kJ: \(\boldsymbol{628}\)
• Baked Potato:
• cal: \(\boldsymbol{2.20 \times 10^5}\)
• kcal: \(\boldsymbol{220.}\)