Question

complete the following table. be sure each of your answer entries has the correct number of significant digits. a cup of cooked white rice an ounce of breakfast corn flakes a chocolate chip cookie

Explanation:

To solve this, we use the conversion factors: \( 1\ \text{kcal} = 1000\ \text{cal} = 1\ \text{Cal} \) (note: sometimes "cal" can be confusing, but here we use \( 1\ \text{kcal} = 10^3\ \text{cal} \)) and \( 1\ \text{kcal} = 4.184\ \text{kJ} \) (or sometimes approximated as \( 4.18\ \text{kJ} \) or \( 4.186\ \text{kJ} \); we'll use \( 4.184\ \text{kJ/kcal} \) for accuracy).

Part 1: A cup of cooked white rice

Given: \( \text{cal} = 2.25 \times 10^5 \)

Step 1: Convert cal to kcal

Since \( 1\ \text{kcal} = 1000\ \text{cal} \), divide by \( 10^3 \):

$$ \text{kcal} = \frac{2.25 \times 10^5}{10^3} = 2.25 \times 10^2 = 225 $$

Step 2: Convert kcal to kJ

Use \( 1\ \text{kcal} = 4.184\ \text{kJ} \):

$$ \text{kJ} = 225\ \text{kcal} \times 4.184\ \text{kJ/kcal} = 941.4\ \text{kJ} \approx 9.41 \times 10^2\ \text{kJ} \ (\text{or}\ 941\ \text{kJ}) $$

Part 2: An ounce of breakfast corn flakes

Given: \( \text{kcal} = 110. \) (the decimal implies 3 significant digits)

Step 1: Convert kcal to cal

Multiply by \( 10^3 \):

$$ \text{cal} = 110. \times 10^3 = 1.10 \times 10^5 $$

Step 2: Convert kcal to kJ

Use \( 1\ \text{kcal} = 4.184\ \text{kJ} \):

$$ \text{kJ} = 110.\ \text{kcal} \times 4.184\ \text{kJ/kcal} = 460.24\ \text{kJ} \approx 4.60 \times 10^2\ \text{kJ} \ (\text{or}\ 460\ \text{kJ}) $$

Part 3: A chocolate chip cookie

Given: \( \text{kJ} = 188. \) (3 significant digits)

Step 1: Convert kJ to kcal

Divide by \( 4.184\ \text{kJ/kcal} \):

$$ \text{kcal} = \frac{188.}{4.184} \approx 44.93\ \text{kcal} \approx 44.9\ \text{kcal} \ (\text{or}\ 45.0\ \text{kcal}\ \text{if using more precise rounding}) $$

Step 2: Convert kcal to cal

Multiply by \( 10^3 \):

$$ \text{cal} = 44.9\ \text{kcal} \times 10^3 = 4.49 \times 10^4\ \text{cal} \ (\text{or}\ 44900\ \text{cal}) $$

Final Table Entries:

Food	cal	kcal	kJ
An ounce of breakfast corn flakes	\( 1.10 \times 10^5 \)	110.	\( 4.60 \times 10^2 \) (or 460)
A chocolate chip cookie	\( 4.49 \times 10^4 \)	44.9	188.

Key Notes on Significant Digits:

• For \( 2.25 \times 10^5\ \text{cal} \), 3 significant digits → kcal (225, 3 sig figs) and kJ (941, 3 sig figs).
• For 110. kcal (3 sig figs) → cal (\( 1.10 \times 10^5 \), 3 sig figs) and kJ (460, 3 sig figs).
• For 188. kJ (3 sig figs) → kcal (44.9, 3 sig figs) and cal (\( 4.49 \times 10^4 \), 3 sig figs).

Final Answers (Filled Table):

1. A cup of cooked white rice:

• kcal: \( \boldsymbol{225} \)
• kJ: \( \boldsymbol{941} \) (or \( 9.41 \times 10^2 \))

1. An ounce of breakfast corn flakes:

• cal: \( \boldsymbol{1.10 \times 10^5} \) (or 110000)
• kJ: \( \boldsymbol{460} \) (or \( 4.60 \times 10^2 \))

1. A chocolate chip cookie:

• cal: \( \boldsymbol{4.49 \times 10^4} \) (or 44900)
• kcal: \( \boldsymbol{44.9} \) (or 45.0)

(Adjust rounding based on textbook conventions; some use \( 1\ \text{kcal} = 4.18\ \text{kJ} \) for simplicity, which would change kJ values slightly.)

Answer:

To solve this, we use the conversion factors: \( 1\ \text{kcal} = 1000\ \text{cal} = 1\ \text{Cal} \) (note: sometimes "cal" can be confusing, but here we use \( 1\ \text{kcal} = 10^3\ \text{cal} \)) and \( 1\ \text{kcal} = 4.184\ \text{kJ} \) (or sometimes approximated as \( 4.18\ \text{kJ} \) or \( 4.186\ \text{kJ} \); we'll use \( 4.184\ \text{kJ/kcal} \) for accuracy).

Part 1: A cup of cooked white rice

Given: \( \text{cal} = 2.25 \times 10^5 \)

Step 1: Convert cal to kcal

Since \( 1\ \text{kcal} = 1000\ \text{cal} \), divide by \( 10^3 \):

$$ \text{kcal} = \frac{2.25 \times 10^5}{10^3} = 2.25 \times 10^2 = 225 $$

Step 2: Convert kcal to kJ

Use \( 1\ \text{kcal} = 4.184\ \text{kJ} \):

$$ \text{kJ} = 225\ \text{kcal} \times 4.184\ \text{kJ/kcal} = 941.4\ \text{kJ} \approx 9.41 \times 10^2\ \text{kJ} \ (\text{or}\ 941\ \text{kJ}) $$

Part 2: An ounce of breakfast corn flakes

Given: \( \text{kcal} = 110. \) (the decimal implies 3 significant digits)

Step 1: Convert kcal to cal

Multiply by \( 10^3 \):

$$ \text{cal} = 110. \times 10^3 = 1.10 \times 10^5 $$

Step 2: Convert kcal to kJ

Use \( 1\ \text{kcal} = 4.184\ \text{kJ} \):

$$ \text{kJ} = 110.\ \text{kcal} \times 4.184\ \text{kJ/kcal} = 460.24\ \text{kJ} \approx 4.60 \times 10^2\ \text{kJ} \ (\text{or}\ 460\ \text{kJ}) $$

Part 3: A chocolate chip cookie

Given: \( \text{kJ} = 188. \) (3 significant digits)

Step 1: Convert kJ to kcal

Divide by \( 4.184\ \text{kJ/kcal} \):

$$ \text{kcal} = \frac{188.}{4.184} \approx 44.93\ \text{kcal} \approx 44.9\ \text{kcal} \ (\text{or}\ 45.0\ \text{kcal}\ \text{if using more precise rounding}) $$

Step 2: Convert kcal to cal

Multiply by \( 10^3 \):

$$ \text{cal} = 44.9\ \text{kcal} \times 10^3 = 4.49 \times 10^4\ \text{cal} \ (\text{or}\ 44900\ \text{cal}) $$

Final Table Entries:

Food	cal	kcal	kJ
An ounce of breakfast corn flakes	\( 1.10 \times 10^5 \)	110.	\( 4.60 \times 10^2 \) (or 460)
A chocolate chip cookie	\( 4.49 \times 10^4 \)	44.9	188.

Key Notes on Significant Digits:

• For \( 2.25 \times 10^5\ \text{cal} \), 3 significant digits → kcal (225, 3 sig figs) and kJ (941, 3 sig figs).
• For 110. kcal (3 sig figs) → cal (\( 1.10 \times 10^5 \), 3 sig figs) and kJ (460, 3 sig figs).
• For 188. kJ (3 sig figs) → kcal (44.9, 3 sig figs) and cal (\( 4.49 \times 10^4 \), 3 sig figs).

Final Answers (Filled Table):

1. A cup of cooked white rice:

• kcal: \( \boldsymbol{225} \)
• kJ: \( \boldsymbol{941} \) (or \( 9.41 \times 10^2 \))

1. An ounce of breakfast corn flakes:

• cal: \( \boldsymbol{1.10 \times 10^5} \) (or 110000)
• kJ: \( \boldsymbol{460} \) (or \( 4.60 \times 10^2 \))

1. A chocolate chip cookie:

• cal: \( \boldsymbol{4.49 \times 10^4} \) (or 44900)
• kcal: \( \boldsymbol{44.9} \) (or 45.0)

(Adjust rounding based on textbook conventions; some use \( 1\ \text{kcal} = 4.18\ \text{kJ} \) for simplicity, which would change kJ values slightly.)