VIPSolutionsAct like a helpful tutor and exlain me : Give step-by-step solution with explanation and final answer: **10.** How many significant digits are there in 0.00011 cm? **11.** The difference between a student's experimental measurement of the density of sodium chloride and the known density of this compound reflects the __________ of the student’s result. **12.** Which volume has the most uncertainty associated with the measurement? **13.** Bud N. Chemist must determine the density of a mineral sample. His four trials yield densities of 4.77 g/cm³, 4.67 g/cm³, 4.69 g/cm³, and 4.81 g/cm³. Independent studies found the correct density to be 4.75 g/cm³. Which of the following statements represents the best analysis of the data? **14.** As part of an experiment to determine the density of a new plastic developed in her laboratory, Sara Ann Dippity measures the volume of a solid sample. Her four trials yield volumes of 12.37 cm³, 12.41 cm³, 12.39 cm³, and 12.38 cm³. Measurements of other scientists in the lab give an average volume of 12.49 cm³. Which of the following statements represents the best analysis of the data?
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Act like a helpful tutor and exlain me : Give step-by-step solution with explanation and final answer: **10.** How many significant digits are there in 0.00011 cm? **11.** The difference between a student's experimental measurement of the density of sodium chloride and the known density of this compound reflects the __________ of the student’s result. **12.** Which volume has the most uncertainty associated with the measurement? **13.** Bud N. Chemist must determine the density of a mineral sample. His four trials yield densities of 4.77 g/cm³, 4.67 g/cm³, 4.69 g/cm³, and 4.81 g/cm³. Independent studies found the correct density to be 4.75 g/cm³. Which of the following statements represents the best analysis of the data? **14.** As part of an experiment to determine the density of a new plastic developed in her laboratory, Sara Ann Dippity measures the volume of a solid sample. Her four trials yield volumes of 12.37 cm³, 12.41 cm³, 12.39 cm³, and 12.38 cm³. Measurements of other scientists in the lab give an average volume of 12.49 cm³. Which of the following statements represents the best analysis of the data?
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Asked by: Sagar
Created at: 2025-10-01 02:45:56
Asked by: Sagar
Created at: 2025-10-01 02:45:56
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# Step-by-Step Solutions
---
## 10. Significant Digits in .00011 cm
### Step-by-step
1. **Identify nonzero digits**: Only the digits "1" and "1" in .00011 are nonzero.
2. **Leading zeros**: The zeros before the "1"s (i.e., .000) are **not** significant; they just indicate the decimal place.
3. **Count significant digits**: Only the digits "1" and "1" are significant.
**Final Answer:**
> **There are 2 significant digits in .00011 cm.**
---
## 11. Accuracy or Precision?
### Step-by-step
- **Accuracy**: How close a measurement is to the true (known) value.
- **Precision**: How close repeated measurements are to each other.
**Explanation:**
If a student's measurement differs from the known value, this difference reflects the **accuracy** of the student's result.
**Final Answer:**
> **The difference reflects the accuracy of the student’s result.**
---
## 12. Greatest Uncertainty
### Step-by-step
- **Uncertainty** in a measurement is typically associated with the number of significant digits.
- The **fewer significant digits** there are, the **greater the uncertainty**.
**Typical example (not specified):**
- 10 mL (2 sig figs) vs. 10.00 mL (4 sig figs): 10 mL has more uncertainty.
**Final Answer:**
> **The volume with the fewest significant digits has the most uncertainty.**
*(If a list of choices was provided, select the one with the least number of significant digits.)*
---
## 13. Analysis of Bud N. Chemist's Density Data
### Data Given
- Trials: 4.77, 4.67, 4.69, 4.81 g/cm³
- True value: 4.75 g/cm³
#### Step 1: Calculate Average
\[
\text{Average} = \frac{4.77 + 4.67 + 4.69 + 4.81}{4} = \frac{18.94}{4} = 4.735 \text{ g/cm}^3
\]
#### Step 2: Compare for Accuracy
- The average (4.735 g/cm³) is **close to** the true value (4.75 g/cm³), but not exact.
#### Step 3: Examine Precision
- The data points are **fairly close** to each other (difference between highest and lowest: 4.81 - 4.67 = .14).
#### Step 4: Best Analysis
- **The results are both reasonably accurate (close to true value) and reasonably precise (close to each other), but not perfect in either.**
**Final Answer:**
> **The data are both reasonably accurate and reasonably precise.**
---
## 14. Analysis of Sara Ann Dippity's Volume Data
### Data Given
- Trials: 12.37, 12.41, 12.39, 12.38 cm³
- Other scientists' average: 12.49 cm³
#### Step 1: Calculate Average
\[
\text{Average} = \frac{12.37 + 12.41 + 12.39 + 12.38}{4} = \frac{49.55}{4} = 12.3875 \text{ cm}^3
\]
#### Step 2: Compare for Accuracy
- Sara's average (12.39 cm³) is **less** than the lab average (12.49 cm³), so not very accurate.
#### Step 3: Examine Precision
- Sara's results vary only by .04 cm³ (12.37 to 12.41), so her data are **very precise**.
#### Step 4: Best Analysis
- **Her results are precise (consistent with each other), but not accurate (not close to the accepted value).**
**Final Answer:**
> **The data are precise but not accurate.**
---
# Summary Table
| Q# | Answer |
|----|--------|
| 10 | 2 significant digits |
| 11 | Accuracy |
| 12 | The volume with the fewest significant digits (greatest uncertainty) |
| 13 | The data are both reasonably accurate and reasonably precise |
| 14 | The data are precise but not accurate |
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