1. The mass of an object ie found to be (24.5 +_ 0.2)g.
A. Find: Absulute uncertainty (Au)
B Find : Relative uncertainty (Ru
II. The density of an object was found to be 2.7 g/cubic cm +_ 1.5%.
What is the absolute uncertainty of the density of the object?
III. The following are the values obtained in measuring the temperature of a room: 31.0 degree celcius, 30.5 C, 30.0 C, 31.3 C,
30.8 C, 30.6 C, and 31.1 Celcius. What is the room temperature?
Show the step by step procedure in getting the uncertainty.
A. Find: Mean=
B. Find: Range=
C. Find: Uncertainty =
D. What is the room temperature?

Let's go through each part of your question step by step.

---

### I. MASS OF THE OBJECT: (24.5 ± 0.2) g

**A. Find Absolute Uncertainty (Au):**
- The **absolute uncertainty** is the given uncertainty in the measurement, which is already provided as **± 0.2 g**.

Thus,  
**Au = 0.2 g**

**B. Find Relative Uncertainty (Ru):**
- The **relative uncertainty** is the ratio of the absolute uncertainty to the measured value, typically expressed as a percentage.

\[
\text{Ru} = \frac{\text{Absolute Uncertainty (Au)}}{\text{Measured Value}} \times 100
\]

\[
\text{Ru} = \frac{0.2}{24.5} \times 100 \approx 0.82\%
\]

Thus,  
**Ru ≈ 0.82%**

---

### II. DENSITY OF THE OBJECT: 2.7 g/cm³ ± 1.5%

You are given the **relative uncertainty** as **1.5%**, and we need to calculate the **absolute uncertainty**.

**Absolute Uncertainty (Au) in density** can be calculated as:

\[
\text{Au} = \left( \frac{\text{Relative Uncertainty}}{100} \right) \times \text{Measured Value}
\]

\[
\text{Au} = \left( \frac{1.5}{100} \right) \times 2.7 = 0.0405 \, \text{g/cm}^3
\]

Thus,  
**Absolute Uncertainty (Au) = 0.0405 g/cm³**

---

### III. ROOM TEMPERATURE MEASUREMENTS

Given temperature values:  
**31.0°C, 30.5°C, 30.0°C, 31.3°C, 30.8°C, 30.6°C, and 31.1°C**

**A. Find Mean Temperature:**
To find the **mean**, add up all the measurements and divide by the number of measurements.

\[
\text{Mean} = \frac{31.0 + 30.5 + 30.0 + 31.3 + 30.8 + 30.6 + 31.1}{7}
\]

\[
\text{Mean} = \frac{215.3}{7} \approx 30.76 \,^\circ C
\]

Thus,  
**Mean ≈ 30.76°C**

**B. Find Range:**
The **range** is the difference between the maximum and minimum values.

Maximum value = **31.3°C**  
Minimum value = **30.0°C**

\[
\text{Range} = 31.3 - 30.0 = 1.3 \,^\circ C
\]

Thus,  
**Range = 1.3°C**

**C. Find Uncertainty:**
The uncertainty can be estimated as half of the range.

\[
\text{Uncertainty} = \frac{\text{Range}}{2} = \frac{1.3}{2} = 0.65 \,^\circ C
\]

Thus,  
**Uncertainty = 0.65°C**

**D. What is the Room Temperature?**
The room temperature is the **mean value** with the **uncertainty**.

Thus,  
**Room Temperature = (30.76 ± 0.65)°C**

---

### Summary of Results:

1. **Absolute Uncertainty (Au)** of mass = **0.2 g**  
2. **Relative Uncertainty (Ru)** of mass ≈ **0.82%**  
3. **Absolute Uncertainty (Au)** of density ≈ **0.0405 g/cm³**  
4. **Mean Room Temperature** ≈ **30.76°C**  
5. **Range** = **1.3°C**  
6. **Uncertainty** = **0.65°C**  
7. **Room Temperature** ≈ **(30.76 ± 0.65)°C**

---

Let me know if you'd like further clarification on any part or have any questions!

### Related Questions:
1. How do you calculate relative uncertainty if given an absolute error?
2. Why is range used to estimate uncertainty in repeated measurements?
3. What is the significance of uncertainty in scientific measurements?
4. Can you convert relative uncertainty to absolute uncertainty in any context?
5. How do you interpret the final room temperature with its uncertainty?

### Tip: 
In measurements, always express the final result with its uncertainty to reflect the precision of your data.

1. The mass of an object is found to be (24.5 ± 0.2)g. A. Find: Absolute uncertainty (Au) B. Find: Relative uncertainty (Ru) II. The density of an object was found to be 2.7 g/cubic cm ± 1.5%. What is the absolute uncertainty of the density of the object? III. The following are the values obtained in measuring the temperature of a room: 31.0°C, 30.5°C, 30.0°C, 31.3°C, 30.8°C, 30.6°C, and 31.1°C. What is the room temperature? Show the step-by-step procedure in getting the uncertainty. A. Find: Mean= B. Find: Range= C. Find: Uncertainty= D. What is the room temperature?

Learn how to calculate absolute and relative uncertainty in mass and density measurements, as well as the mean, range, and uncertainty of room temperature measurements. This step-by-step guide covers key concepts in uncertainty and basic statistics, ideal for high school students in Grades 10-12.

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