calculations using significant figures
when multiplying and dividing, limit and round to the least number of significant figures
in any of the factors.
example 1: 23.0 cm × 432 cm × 19 cm = 188,784 cm³
the answer is expressed as 190,000 cm³ since 19 cm has only two
significant figures.
when adding and subtracting, limit and round your answer to the least number of
decimal places in any of the numbers that make up your answer.
example 2: 123.25 ml + 46.0 ml + 86.257 ml = 255.507 ml
the answer is expressed as 255.5 ml since 46.0 ml has only one
decimal place.
perform each operation, expressing the answer in the correct number of significant figures.
1. 1.35 m × 2.467 m = ________
2. 1,035 m² ÷ 42 m = ________
3. 12.01 ml + 35.2 ml + 6 ml = ________
4. 55.46 g − 28.9 g = ________
5. 0.021 cm × 3.2 cm × 100.1 cm = ________
6. 0.15 cm + 1.15 cm + 2.051 cm = ________
7. 150 l³ ÷ 4 l = ________
8. 505 kg − 450.25 kg = ________
9. 1.252 mm × 0.115 mm × 0.012 mm = ________
10. 1.278 × 10³ m² ÷ 1.4267 × 10² m = ________

Question

calculations using significant figures
when multiplying and dividing, limit and round to the least number of significant figures
in any of the factors.
    example 1: 23.0 cm × 432 cm × 19 cm = 188,784 cm³
               the answer is expressed as 190,000 cm³ since 19 cm has only two
               significant figures.
when adding and subtracting, limit and round your answer to the least number of
decimal places in any of the numbers that make up your answer.
    example 2: 123.25 ml + 46.0 ml + 86.257 ml = 255.507 ml
               the answer is expressed as 255.5 ml since 46.0 ml has only one
               decimal place.
perform each operation, expressing the answer in the correct number of significant figures.
1.  1.35 m × 2.467 m = ________
2.  1,035 m² ÷ 42 m = ________
3.  12.01 ml + 35.2 ml + 6 ml = ________
4.  55.46 g − 28.9 g = ________
5.  0.021 cm × 3.2 cm × 100.1 cm = ________
6.  0.15 cm + 1.15 cm + 2.051 cm = ________
7.  150 l³ ÷ 4 l = ________
8.  505 kg − 450.25 kg = ________
9.  1.252 mm × 0.115 mm × 0.012 mm = ________
10. 1.278 × 10³ m² ÷ 1.4267 × 10² m = ________

Accepted Answer

### Problem 1: $ 1.35 \, \text{m} \times 2.467 \, \text{m} $
# Explanation:
## Step 1: Multiply the numbers
$ 1.35 \times 2.467 = 3.33045 $
## Step 2: Determine significant figures
1.35 has 3 significant figures, 2.467 has 4. Round to 3 significant figures.
$ 3.33045 \approx 3.33 $
# Answer: $ 3.33 \, \text{m}^2 $

### Problem 2: $ 1035 \, \text{m}^2 \div 42 \, \text{m} $ (assuming 1,035 is 1035)
# Explanation:
## Step 1: Divide the numbers
$ 1035 \div 42 = 24.642857\ldots $
## Step 2: Determine significant figures
1035 has 4, 42 has 2. Round to 2 significant figures.
$ 24.642857\ldots \approx 25 $ (wait, 24.64... rounded to 2 sig figs is 25? Wait, 24.64, first two sig figs are 2 and 4, the next digit is 6 which is more than 5, so round up 4 to 5. So 25. But wait, 1035 is 4 sig figs, 42 is 2. So result should have 2. So 25 (or 2.5 × 10¹? Wait, 1035 ÷ 42 = 24.64..., so 25 when rounded to 2 sig figs. Wait, 24.64, the first two significant figures are 2 and 4. The third digit is 6, which is greater than 5, so we round the second digit (4) up to 5. So 25.
# Answer: $ 25 \, \text{m} $ (or $ 2.5 \times 10^1 \, \text{m} $)

### Problem 3: $ 12.01 \, \text{mL} + 35.2 \, \text{mL} + 6 \, \text{mL} $
# Explanation:
## Step 1: Add the numbers
$ 12.01 + 35.2 + 6 = 53.21 $
## Step 2: Determine decimal places
12.01 has 2 decimal places, 35.2 has 1, 6 has 0. Round to 0 decimal places (least number of decimal places is 0 from 6).
$ 53.21 \approx 53 $
# Answer: $ 53 \, \text{mL} $

### Problem 4: $ 55.46 \, \text{g} - 28.9 \, \text{g} $
# Explanation:
## Step 1: Subtract the numbers
$ 55.46 - 28.9 = 26.56 $
## Step 2: Determine decimal places
55.46 has 2, 28.9 has 1. Round to 1 decimal place.
$ 26.56 \approx 26.6 $
# Answer: $ 26.6 \, \text{g} $

### Problem 5: $ 0.021 \, \text{cm} \times 3.2 \, \text{cm} \times 100.1 \, \text{cm} $
# Explanation:
## Step 1: Multiply the numbers
$ 0.021 \times 3.2 = 0.0672 $; $ 0.0672 \times 100.1 = 6.72672 $
## Step 2: Determine significant figures
0.021 has 2, 3.2 has 2, 100.1 has 4. Round to 2 significant figures.
$ 6.72672 \approx 6.7 $
# Answer: $ 6.7 \, \text{cm}^3 $

### Problem 6: $ 0.15 \, \text{cm} + 1.15 \, \text{cm} + 2.051 \, \text{cm} $
# Explanation:
## Step 1: Add the numbers
$ 0.15 + 1.15 + 2.051 = 3.351 $
## Step 2: Determine decimal places
0.15 has 2, 1.15 has 2, 2.051 has 3. Round to 2 decimal places.
$ 3.351 \approx 3.35 $
# Answer: $ 3.35 \, \text{cm} $

### Problem 7: $ 150 \, \text{L}^3 \div 4 \, \text{L} $ (assuming 150 L³ is 150 L³, but units: L³ ÷ L = L²)
# Explanation:
## Step 1: Divide the numbers
$ 150 \div 4 = 37.5 $
## Step 2: Determine significant figures
150 has 2 (if the zero is not significant) or 3 (if it is). 4 has 1. Wait, 150: trailing zero without decimal is ambiguous, but often considered 2 sig figs. 4 has 1. Wait, maybe 150 is 3 sig figs (if written as 150.), but here it's 150. So maybe 2 or 3. But 4 has 1. So round to 1 significant figure? Wait, 150 ÷ 4 = 37.5. If 4 has 1 sig fig, result should have 1. So 40 (or 4 × 10¹). But maybe 150 is 3 sig figs (1,5,0 with decimal implied? No, it's 150). Alternatively, maybe the problem has 150 as 2 sig figs (1 and 5, zero is placeholder). 4 has 1. So 37.5 rounded to 1 sig fig is 40.
# Answer: $ 40 \, \text{L}^2 $ (or $ 4 \times 10^1 \, \text{L}^2 $)

### Problem 8: $ 505 \, \text{kg} - 450.25 \, \text{kg} $
# Explanation:
## Step 1: Subtract the numbers
$ 505 - 450.25 = 54.75 $
## Step 2: Determine decimal places
505 has 0, 450.25 has 2. Round to 0 decimal places.
$ 54.75 \approx 55 $
# Answer: $ 55 \, \text{kg} $

### Problem 9: $ 1.252 \, \text{mm} \times 0.115 \, \text{mm} \times 0.012 \, \text{mm} $
# Explanation:
## Step 1: Multiply the numbers
$ 1.252 \times 0.115 = 0.14398 $; $ 0.14398 \times 0.012 = 0.00172776 $
## Step 2: Determine significant figures
1.252 has 4, 0.115 has 3, 0.012 has 2. Round to 2 significant figures.
$ 0.00172776 \approx 0.0017 $ (or $ 1.7 \times 10^{-3} $)
# Answer: $ 1.7 \times 10^{-3} \, \text{mm}^3 $ (or $ 0.0017 \, \text{mm}^3 $)

### Problem 10: $ 1.278 \times 10^3 \, \text{m}^2 \div 1.4267 \times 10^2 \, \text{m} $
# Explanation:
## Step 1: Divide the numbers (and exponents)
$ \frac{1.278 \times 10^3}{1.4267 \times 10^2} = \frac{1.278}{1.4267} \times 10^{3 - 2} \approx 0.8958 \times 10^1 = 8.958 $
## Step 2: Determine significant figures
1.278 has 4, 1.4267 has 5. Round to 4 significant figures? Wait, 1.278 (4) and 1.4267 (5), so result should have 4. Wait, 0.8958 × 10¹ = 8.958. Wait, 1.278 ÷ 1.4267 ≈ 0.8958, times 10 is 8.958. 1.278 has 4 sig figs, 1.4267 has 5, so the limiting is 4. So 8.958 rounded to 4 sig figs is 8.958? Wait, 0.8958 × 10¹ = 8.958. Wait, 1.278 (4) and 1.4267 (5), so the number of sig figs is 4. So 8.958 (which is 4 sig figs: 8,9,5,8). Wait, maybe I made a mistake. Let's recalculate: 1.278 × 10³ = 1278, 1.4267 × 10² = 142.67. 1278 ÷ 142.67 ≈ 8.958. So 8.96 (if 3 sig figs? Wait, 1.278 has 4, 1.4267 has 5. So the result should have 4 sig figs. So 8.958 (which is 4 sig figs). Wait, 8.958 is 4 significant figures. So the answer is approximately 8.96 (if rounded to 3? Wait, no: 1.278 (4) and 1.4267 (5), so the least is 4. So 8.958 (4 sig figs) or 8.96 (3)? Wait, maybe the problem expects 3. Let's check: 1.278 ÷ 1.4267 ≈ 0.8958, times 10 is 8.958. 1.278 has 4, 1.4267 has 5. So 4 sig figs: 8.958. But maybe 8.96 (3 sig figs) if 1.278 is considered 3? Wait, 1.278 is 4. So 8.958, which can be written as 8.96 (3) or 8.958 (4). Let's go with 4: 8.958, or 8.96 (3). Maybe the intended is 8.96.
# Answer: $ 8.96 \, \text{m} $ (or $ 8.958 \, \text{m} $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 1.35 \, \text{m} \times 2.467 \, \text{m} \)

Step 1: Multiply the numbers

Step 2: Determine significant figures

Step 1: Divide the numbers

Step 2: Determine significant figures

Step 1: Add the numbers

Step 2: Determine decimal places

Answer:

Problem 2: \( 1035 \, \text{m}^2 \div 42 \, \text{m} \) (assuming 1,035 is 1035)