Question

complete the following table. be sure each of your answer entries has the correct number of significant digits.

food	energy content when eaten
a cup of cooked white rice	$2.25 \times 10^5$
a 12-ounce soft drink		150.
a cup of chicken noodle soup			314.

Explanation:

Step1: Recall unit conversions

We know that \( 1\ \text{kcal} = 1000\ \text{cal} = 4.184\ \text{kJ} \)

Step2: For a cup of cooked white rice (cal to kcal)

Given \( \text{cal} = 2.25\times 10^{5}\ \text{cal} \), to convert to kcal, we use \( 1\ \text{kcal} = 1000\ \text{cal} \), so \( \text{kcal}=\frac{2.25\times 10^{5}}{1000}= 225\ \text{kcal} \)

Step3: For a cup of cooked white rice (kcal to kJ)

Using \( 1\ \text{kcal} = 4.184\ \text{kJ} \), so \( \text{kJ}=225\times4.184 = 941.4\ \text{kJ}\approx9.41\times 10^{2}\ \text{kJ} \) (or keep as 941 kJ with appropriate sig figs)

Step4: For a 12 - ounce soft drink (kcal to cal)

Given \( \text{kcal} = 150\ \text{kcal} \), since \( 1\ \text{kcal}=1000\ \text{cal} \), \( \text{cal}=150\times 1000 = 1.5\times 10^{5}\ \text{cal} \)

Step5: For a 12 - ounce soft drink (kcal to kJ)

Using \( 1\ \text{kcal} = 4.184\ \text{kJ} \), \( \text{kJ}=150\times4.184=627.6\ \text{kJ}\approx6.28\times 10^{2}\ \text{kJ} \) (or 628 kJ)

Step6: For a cup of chicken noodle soup (kJ to kcal)

Given \( \text{kJ} = 314\ \text{kJ} \), using \( 1\ \text{kcal}=\frac{1}{4.184}\ \text{kJ} \), \( \text{kcal}=\frac{314}{4.184}\approx75.0\ \text{kcal} \)

Step7: For a cup of chicken noodle soup (kcal to cal)

Since \( 1\ \text{kcal} = 1000\ \text{cal} \), \( \text{cal}=75.0\times 1000 = 7.5\times 10^{4}\ \text{cal} \)

Filling the table:

• a cup of cooked white rice:
• \( \text{kcal} = 225 \)
• \( \text{kJ}=941 \) (or \( 9.41\times 10^{2} \))
• a 12 - ounce soft drink:
• \( \text{cal}=1.5\times 10^{5} \)
• \( \text{kJ}=628 \) (or \( 6.28\times 10^{2} \))
• a cup of chicken noodle soup:
• \( \text{cal}=7.5\times 10^{4} \)
• \( \text{kcal}=75.0 \)

Answer:

food	cal	kcal	kJ
a 12 - ounce soft drink	\( 1.5\times 10^{5} \)	150	\( 6.28\times 10^{2} \)
a cup of chicken noodle soup	\( 7.5\times 10^{4} \)	75.0	314

(Note: The values are filled based on unit conversions. The significant figures and exact values can be adjusted based on the problem's requirement. For example, the conversion factor \( 4.184\ \text{kJ/kcal} \) can be approximated as \( 4.18\) or \( 4.2\) for simplicity in some cases, which may slightly change the results.)