Question

2.27 × 2.2 = ?
2.27/2.2 = ?
2.27 + 2.2 = ?
2.27 − 2.2 = ?
incorrect rounding
5.0 cm³
1.0
1.03
4.5 cm
0.07 cm
4.47 cm
0.0 cm
4.99 cm²
4.994 cm²
0.1 cm
submit
previous answers
incorrect; try again; 7 attempts remaining
you sorted 3 out of 11 items incorrectly recall that while performing a division operation, you round off the answer to the same number of significant figures has the lowest significant figures. the correct answer should have the same number of significant figures as that in 2.2 cm

Answer:

To solve these problems, we'll apply significant figure rules for each operation (multiplication/division, addition/subtraction).

1. \( 2.27 \times 2.2 = ? \)

Step 1: Perform the multiplication

\( 2.27 \times 2.2 = 4.994 \)

Step 2: Apply significant figures (multiplication: least number of significant figures in factors)

\( 2.27 \) has 3 sig figs, \( 2.2 \) has 2 sig figs. Round to 2 sig figs: \( 5.0 \) (since \( 4.994 \approx 5.0 \) with 2 sig figs).

2. \( 2.27 / 2.2 = ? \)

Step 1: Perform the division

\( 2.27 \div 2.2 \approx 1.0318 \)

Step 2: Apply significant figures (division: least number of significant figures in factors)

\( 2.2 \) has 2 sig figs. Round to 2 sig figs: \( 1.0 \) (not \( 1.03 \), which has 3 sig figs).

3. \( 2.27 + 2.2 = ? \)

Step 1: Perform the addition

\( 2.27 + 2.2 = 4.47 \)

Step 2: Apply significant figures (addition: least number of decimal places)

\( 2.27 \) has 2 decimal places, \( 2.2 \) has 1 decimal place. Round to 1 decimal place: \( 4.5 \) (since \( 4.47 \approx 4.5 \) with 1 decimal place).

4. \( 2.27 - 2.2 = ? \)

Step 1: Perform the subtraction

\( 2.27 - 2.2 = 0.07 \)

Step 2: Apply significant figures (subtraction: least number of decimal places)

\( 2.2 \) has 1 decimal place, but the result \( 0.07 \) has 2 significant figures (the trailing zero before 7 is not significant, but 7 is). Wait, actually, \( 2.27 - 2.2 = 0.07 \), which is correct as is (since the uncertainty is in the hundredths place for \( 2.27 \), but \( 2.2 \) is to the tenths place—so the result should have precision to the tenths place? Wait, no: \( 2.27 \) is to the hundredth, \( 2.2 \) to the tenth. The result’s precision is limited by the least precise measurement (tenth place). But \( 2.27 - 2.2 = 0.07 \), which is 0.07 (two significant figures? Wait, \( 2.2 \) has two significant figures, \( 2.27 \) has three. For subtraction, we look at decimal places: \( 2.2 \) has 1 decimal place, \( 2.27 \) has 2. So the result should be rounded to 1 decimal place? Wait, \( 0.07 \) is 0.1 when rounded to 1 decimal place? Wait, no—\( 0.07 \) is 0.1 when rounded to one decimal place? Wait, \( 0.07 \) is 0.1 (since the first decimal place is 0, the second is 7, so round up the first decimal place: 0.1). Wait, maybe I made a mistake earlier. Let’s recheck:

\( 2.27 - 2.2 = 0.07 \). The number \( 2.2 \) has one decimal place, so the result should have one decimal place. \( 0.07 \) rounded to one decimal place is \( 0.1 \) (because the tenths place is 0, the hundredths is 7, so we round up the tenths place: \( 0.1 \)). Wait, but the original calculation gives \( 0.07 \), but with significant figures for subtraction, we go by decimal places. So \( 2.2 \) (1 decimal place) and \( 2.27 \) (2 decimal places) → result should have 1 decimal place. So \( 0.07 \) rounded to 1 decimal place is \( 0.1 \).

5. Incorrect Rounding Group

We need to identify which values are incorrectly rounded. Let’s analyze each:

• \( 4.47 \, \text{cm} \): From \( 2.27 + 2.2 = 4.47 \), which should be rounded to \( 4.5 \, \text{cm} \) (1 decimal place). So \( 4.47 \) is incorrect (not rounded).
• \( 0.0 \, \text{cm} \): From \( 2.27 - 2.2 = 0.07 \), which should be \( 0.1 \, \text{cm} \) (1 decimal place). \( 0.0 \) is incorrect.
• \( 4.99 \, \text{cm}^2 \): From \( 2.27 \times 2.2 = 4.994 \), which should be \( 5.0 \, \text{cm}^2 \) (2 sig figs). \( 4.99 \) is incorrect (3 sig figs).
• \( 4.994 \, \text{cm}^2 \): From \( 2.27 \times 2.2 = 4.994 \), which should be rounded to \( 5.0 \, \text{cm}^2 \) (2 sig figs). \( 4.994 \) is incorrect (not rounded).
• \( 0.1 \, \text{cm} \): Correct (from \( 2.27 - 2.2 = 0.07 \), rounded to 1 decimal place).

Correct Sorting:

• \( 2.27 \times 2.2 \): \( 5.0 \, \text{cm}^2 \) (correct).
• \( 2.27 / 2.2 \): \( 1.0 \) (correct, not \( 1.03 \)).
• \( 2.27 + 2.2 \): \( 4.5 \, \text{cm} \) (correct).
• \( 2.27 - 2.2 \): \( 0.1 \, \text{cm} \) (correct, not \( 0.07 \)).
• Incorrect Rounding: \( 4.47 \, \text{cm} \), \( 0.0 \, \text{cm} \), \( 4.99 \, \text{cm}^2 \), \( 4.994 \, \text{cm}^2 \), \( 0.07 \, \text{cm} \), \( 1.03 \) (wait, the original problem has a “1” next to \( 0.0 \, \text{cm} \)—maybe a typo, but focus on significant figures).

Final Answers (for each operation):

1. \( 2.27 \times 2.2 = \boldsymbol{5.0 \, \text{cm}^2} \)
2. \( 2.27 / 2.2 = \boldsymbol{1.0} \)
3. \( 2.27 + 2.2 = \boldsymbol{4.5 \, \text{cm}} \)
4. \( 2.27 - 2.2 = \boldsymbol{0.1 \, \text{cm}} \)
5. Incorrectly rounded: \( 4.47 \, \text{cm} \), \( 0.0 \, \text{cm} \), \( 4.99 \, \text{cm}^2 \), \( 4.994 \, \text{cm}^2 \), \( 0.07 \, \text{cm} \), \( 1.03 \)