2. for multipl... with the least amount of signi... (table with addition, subtraction, multiplication, division examples) practice: perform each of the following calculations, expressing the answer to the correct number of significant figures. be sure to include proper units. 1) 3.482 cm + 8.51 cm + 16.324 cm 2) 48.0032 g + 9.17 g + 65.4321g 3) 80.4 cm − 16.532 cm 4) 106.5 ml − 30. ml 5) 48.2 cm x 1.6 cm x 2.12 cm 6) 8.3 m x 4.0 m x 0.9823 m 7) 64.34 cm³ ÷ 8.149 cm 8) 4.93 mm² ÷ 18.71 mm 9) ( 0.57ml imes \frac{760mm}{740mm} imes \frac{273k}{250k} ) 10) ( 5.13g imes \frac{44.962u}{115.874u} )

Question

2. for multipl... with the least amount of signi... (table with addition, subtraction, multiplication, division examples) practice: perform each of the following calculations, expressing the answer to the correct number of significant figures. be sure to include proper units. 1) 3.482 cm + 8.51 cm + 16.324 cm 2) 48.0032 g + 9.17 g + 65.4321g 3) 80.4 cm − 16.532 cm 4) 106.5 ml − 30. ml 5) 48.2 cm x 1.6 cm x 2.12 cm 6) 8.3 m x 4.0 m x 0.9823 m 7) 64.34 cm³ ÷ 8.149 cm 8) 4.93 mm² ÷ 18.71 mm 9) ( 0.57ml 	imes \frac{760mm}{740mm} 	imes \frac{273k}{250k} ) 10) ( 5.13g 	imes \frac{44.962u}{115.874u} )

Accepted Answer

### 1) $ 3.482\ \text{cm} + 8.51\ \text{cm} + 16.324\ \text{cm} $
# Explanation:
## Step1: Add the numbers
$ 3.482 + 8.51 + 16.324 = 28.316 $
## Step2: Determine significant figures (addition: least decimal places is 2 from 8.51)
Round to two decimal places.
$ 28.316 \approx 28.32 $
# Answer: $ 28.32\ \text{cm} $

### 2) $ 48.0032\ \text{g} + 9.17\ \text{g} + 65.4321\ \text{g} $
# Explanation:
## Step1: Add the numbers
$ 48.0032 + 9.17 + 65.4321 = 122.6053 $
## Step2: Determine significant figures (addition: least decimal places is 2 from 9.17)
Round to two decimal places.
$ 122.6053 \approx 122.61 $
# Answer: $ 122.61\ \text{g} $

### 3) $ 80.4\ \text{cm} - 16.532\ \text{cm} $
# Explanation:
## Step1: Subtract the numbers
$ 80.4 - 16.532 = 63.868 $
## Step2: Determine significant figures (subtraction: least decimal places is 1 from 80.4)
Round to one decimal place.
$ 63.868 \approx 63.9 $
# Answer: $ 63.9\ \text{cm} $

### 4) $ 106.5\ \text{mL} - 30.\ \text{mL} $
# Explanation:
## Step1: Subtract the numbers
$ 106.5 - 30. = 76.5 $
## Step2: Determine significant figures (subtraction: least decimal places is 1 from 106.5, 30. has one significant figure? Wait, 30. has two? Wait, 30. is two sig figs (the decimal shows the zero is significant). Wait, 106.5 has four, 30. has two. Wait, subtraction: decimal places. 106.5 has one decimal place, 30. has zero. So least decimal places is zero? Wait, no: 30. is 3.0 x 10^1, so decimal place is zero? Wait, 106.5 - 30. = 76.5. But 30. has two significant figures? Wait, maybe the 30. is two sig figs (the decimal indicates the zero is significant). But in subtraction, we look at decimal places. 106.5 has 1 decimal place, 30. has 0. So the result should have 0 decimal places? Wait, no, 30. is 30.0? No, 30. is two sig figs. Wait, maybe the problem considers 30. as two sig figs, but in subtraction, decimal places: 106.5 (1 decimal), 30. (0 decimals). So the result should be rounded to 0 decimal places? 76.5 rounded to 0 decimal places is 77? Wait, no, 106.5 - 30. = 76.5. If 30. is two sig figs, but in subtraction, the rule is decimal places. 106.5 has 1, 30. has 0. So the answer should have 0 decimal places. So 77 mL? Wait, maybe the original problem's 30. is two sig figs, but the subtraction: 106.5 - 30. = 76.5. Rounded to the least number of decimal places, which is 0 (from 30.). So 77 mL? Wait, but 30. has two sig figs, 106.5 has four. Wait, maybe I made a mistake. Let's check: 106.5 - 30. = 76.5. The number with the least decimal places is 30. (0 decimal places), so we round 76.5 to 0 decimal places: 77 mL.
# Answer: $ 77\ \text{mL} $

### 5) $ 48.2\ \text{cm} \times 1.6\ \text{cm} \times 2.12\ \text{cm} $
# Explanation:
## Step1: Multiply the numbers
$ 48.2 \times 1.6 = 77.12 $; $ 77.12 \times 2.12 = 163.4944 $
## Step2: Determine significant figures (multiplication: least number of sig figs is 2 from 1.6)
Round to two significant figures? Wait, 48.2 has three, 1.6 has two, 2.12 has three. So least is two? Wait, no: 1.6 has two, so the result should have two? Wait, 48.2 x 1.6 = 77.12 (three sig figs from 48.2, two from 1.6: so two? Wait, no, when multiplying, the result has the same number of sig figs as the least precise measurement. 1.6 has two, so 48.2 x 1.6 = 77 (two sig figs)? Wait, no, 48.2 x 1.6 = 77.12, which should be 77 (two sig figs). Then 77 x 2.12 = 163.24, which with two sig figs is 160? Wait, no, maybe I messed up. Wait, 48.2 (3), 1.6 (2), 2.12 (3). The least is 2, so the final answer should have two sig figs. Wait, but 48.2 x 1.6 x 2.12 = 48.2 x 3.392 = 163.4944. Rounded to two sig figs: 160? But 1.6 is two, so maybe. Wait, but maybe the 1.6 is two, 48.2 is three, 2.12 is three. So the least is two, so two sig figs. So 1.6 x 10^2 cm³? Wait, no, 163.4944 rounded to two sig figs is 160, but written as 1.6 x 10²? Or 160? Wait, maybe the correct approach is: 48.2 (3) x 1.6 (2) x 2.12 (3) = (48.2 x 1.6) x 2.12 = 77.12 (which should be 77, two sig figs) x 2.12 = 163.24, which is 160 (two sig figs). But maybe the problem expects three sig figs? Wait, 1.6 has two, so no. Wait, maybe I made a mistake. Let's recalculate: 48.2 x 1.6 = 77.12 (three sig figs from 48.2, two from 1.6: so two sig figs: 77). Then 77 x 2.12 = 163.24, which with two sig figs is 160. But 160 has two sig figs (the trailing zero is not significant). Alternatively, maybe the 1.6 is two, 48.2 is three, 2.12 is three. So the product should have two sig figs. So 1.6 x 10² cm³. But maybe the answer is 160 cm³ or 1.6 x 10² cm³. Wait, let's check the multiplication again: 48.2 * 1.6 = 77.12; 77.12 * 2.12 = 163.4944. The least number of sig figs is 2 (from 1.6), so we round 163.4944 to two sig figs: 160 (which is 1.6 x 10²). But maybe the problem considers 1.6 as two, 48.2 as three, 2.12 as three, so the result should have two sig figs. So 160 cm³.
# Answer: $ 1.6 \times 10^2\ \text{cm}^3 $ (or $ 160\ \text{cm}^3 $)

### 6) $ 8.3\ \text{m} \times 4.0\ \text{m} \times 0.9823\ \text{m} $
# Explanation:
## Step1: Multiply the numbers
$ 8.3 \times 4.0 = 33.2 $; $ 33.2 \times 0.9823 = 32.61236 $
## Step2: Determine significant figures (multiplication: least number of sig figs is 2 from 8.3 and 4.0 (4.0 has two? Wait, 4.0 has two sig figs (the zero is significant). 8.3 has two, 0.9823 has four. So least is two. Wait, 4.0 has two, 8.3 has two, so the result should have two sig figs.
$ 32.61236 \approx 33 $ (two sig figs)
# Answer: $ 33\ \text{m}^3 $

### 7) $ 64.34\ \text{cm}^3 \div 8.149\ \text{cm} $
# Explanation:
## Step1: Divide the numbers
$ \frac{64.34}{8.149} \approx 7.895 $
## Step2: Determine significant figures (division: least number of sig figs is 4 from 64.34 and 4 from 8.149? Wait, 64.34 has four, 8.149 has four. Wait, no: 64.34 (four), 8.149 (four). So the result should have four? Wait, no, 64.34 ÷ 8.149 ≈ 7.895. Wait, maybe I made a mistake. Wait, 64.34 has four sig figs, 8.149 has four, so the result should have four? But 7.895 is four sig figs. Wait, but maybe the problem expects three? Wait, 64.34 (four), 8.149 (four), so four. But let's check the calculation: 64.34 ÷ 8.149 ≈ 7.895. Rounded to four sig figs is 7.895, but maybe three? Wait, no, the rule is that the result has the same number of sig figs as the least precise measurement. Both have four, so four. But maybe the problem considers 64.34 as four and 8.149 as four, so the answer is 7.895 cm²? Wait, 64.34 cm³ ÷ 8.149 cm = 7.895 cm² (since cm³ / cm = cm²). So 7.895 cm², which with four sig figs is 7.895, but maybe rounded to three? Wait, 64.34 has four, 8.149 has four, so four. So 7.895 cm².
# Answer: $ 7.895\ \text{cm}^2 $ (or $ 7.90\ \text{cm}^2 $ if rounded to three sig figs)

### 8) $ 4.93\ \text{mm}^2 \div 18.71\ \text{mm} $
# Explanation:
## Step1: Divide the numbers
$ \frac{4.93}{18.71} \approx 0.2635 $
## Step2: Determine significant figures (division: least number of sig figs is 3 from 4.93 and 4 from 18.71. So least is 3.
Round to three sig figs: $ 0.2635 \approx 0.264 $
# Answer: $ 0.264\ \text{mm} $

### 9) $ 0.57\ \text{mL} \times \frac{760\ \text{mm}}{740\ \text{mm}} \times \frac{273\ \text{K}}{250\ \text{K}} $
# Explanation:
## Step1: Simplify the fractions
$ \frac{760}{740} \approx 1.027 $; $ \frac{273}{250} = 1.092 $
## Step2: Multiply the numbers
$ 0.57 \times 1.027 \times 1.092 \approx 0.57 \times 1.122 \approx 0.640 $
## Step3: Determine significant figures (multiplication: least number of sig figs is 2 from 0.57)
Round to two sig figs: $ 0.640 \approx 0.64 $
# Answer: $ 0.64\ \text{mL} $

### 10) $ 5.13\ \text{g} \times \frac{44.962\ \text{u}}{115.874\ \text{u}} $
# Explanation:
## Step1: Simplify the fraction
$ \frac{44.962}{115.874} \approx 0.3880 $
## Step2: Multiply the numbers
$ 5.13 \times 0.3880 \approx 1.990 $
## Step3: Determine significant figures (multiplication: least number of sig figs is 3 from 5.13)
Round to three sig figs: $ 1.990 \approx 1.99 $
# Answer: $ 1.99\ \text{g} $

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QUESTION IMAGE

Question

Explanation:

1) \( 3.482\ \text{cm} + 8.51\ \text{cm} + 16.324\ \text{cm} \)

Step1: Add the numbers

Step2: Determine significant figures (addition: least decimal places is 2 from 8.51)

Step1: Add the numbers

Step2: Determine significant figures (addition: least decimal places is 2 from 9.17)

Step1: Subtract the numbers

Step2: Determine significant figures (subtraction: least decimal places is 1 from 80.4)

Answer:

2) \( 48.0032\ \text{g} + 9.17\ \text{g} + 65.4321\ \text{g} \)