Question

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

	energy content when eaten
food	cal	kcal	kj
a slice of cooked bacon	$3.60 \times 10^4$	$\square$	$\square$
a small apple	$\square$	125.	$\square$
a 12-ounce soft drink	$\square$	$\square$	628.

Explanation:

To solve this problem, we need to convert between different units of energy: calories (cal), kilocalories (kcal), and kilojoules (kJ). The key conversion factors are:

• \( 1 \, \text{kcal} = 1000 \, \text{cal} \)
• \( 1 \, \text{kcal} = 4.184 \, \text{kJ} \)

Step 1: Slice of Cooked Bacon

We know the energy in calories is \( 3.60 \times 10^4 \, \text{cal} \).

Convert cal to kcal:

Since \( 1 \, \text{kcal} = 1000 \, \text{cal} \), divide by 1000:
\[
\text{kcal} = \frac{3.60 \times 10^4}{1000} = 36.0 \, \text{kcal}
\]

Convert kcal to kJ:

Using \( 1 \, \text{kcal} = 4.184 \, \text{kJ} \):
\[
\text{kJ} = 36.0 \times 4.184 = 150.624 \approx 151 \, \text{kJ} \, (\text{3 significant figures})
\]

Step 2: Small Apple

We know the energy in kcal is \( 125 \, \text{kcal} \).

Convert kcal to cal:

Multiply by 1000:
\[
\text{cal} = 125 \times 1000 = 1.25 \times 10^5 \, \text{cal}
\]

Convert kcal to kJ:

Using \( 1 \, \text{kcal} = 4.184 \, \text{kJ} \):
\[
\text{kJ} = 125 \times 4.184 = 523 \, \text{kJ} \, (\text{3 significant figures})
\]

Step 3: 12-Ounce Soft Drink

We know the energy in kJ is \( 628 \, \text{kJ} \).

Convert kJ to kcal:

Divide by 4.184:
\[
\text{kcal} = \frac{628}{4.184} \approx 149.9 \approx 150 \, \text{kcal} \, (\text{3 significant figures})
\]

Convert kcal to cal:

Multiply by 1000:
\[
\text{cal} = 150 \times 1000 = 1.50 \times 10^5 \, \text{cal}
\]

Final Table (Filled)

Food	cal	kcal	kJ
Small Apple	\( 1.25 \times 10^5 \)	125	523
12-Ounce Soft Drink	\( 1.50 \times 10^5 \)	150	628

Answer:

s (Filled in Boxes):

• Slice of Cooked Bacon (kcal): \( \boldsymbol{36.0} \)
• Slice of Cooked Bacon (kJ): \( \boldsymbol{151} \)
• Small Apple (cal): \( \boldsymbol{1.25 \times 10^5} \)
• Small Apple (kJ): \( \boldsymbol{523} \)
• 12-Ounce Soft Drink (cal): \( \boldsymbol{1.50 \times 10^5} \)
• 12-Ounce Soft Drink (kcal): \( \boldsymbol{150} \)