4. In the lab, you measure the amount of heat produced from a reaction. You record a value of 70.2 Joules for Substance X. The theoretical answer is actually 68.5 Joules. Calculate your percent error. Show all your calculations and steps used to determine your answer. (3 marks)

Question

5 Complete the following table by stating the number of significant digits and converting the number to scientific notation. (10 marks)

Number

0.00378

3 780

10

0.130

45 000 000

Number of Significant Digits

Scientific Notation

6. Complete the following calculations. Make sure your answer has the correct number of significant digits and/or decimal points. Show all your calculations and steps used to determine your answer. (6 marks)

a. 20.071-(6.3 x 1.222)

b. (9.55 x 10)-(8.476 x 1080)

Answer 1

4. Calculating Percent Error

The formula to calculate percent error is:

\[ \text{Percent Error} = \left( \frac{|\text{Experimental Value} - \text{Theoretical Value}|}{\text{Theoretical Value}} \right) \times 100% \]

Given:

• Experimental Value = 70.2 Joules
• Theoretical Value = 68.5 Joules

Step 1: Calculate the absolute error

\[ |\text{Experimental Value} - \text{Theoretical Value}| = |70.2 - 68.5| = 1.7 \text{ Joules} \]

Step 2: Compute the percent error

\[ \text{Percent Error} = \left( \frac{1.7}{68.5} \right) \times 100% \] \[ \text{Percent Error} = 0.02485 \times 100% = 2.485% \]

Final answer:

\[ \text{Percent Error} \approx 2.49% \quad (\text{rounded to two decimal places}) \]

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5. Significant Digits and Scientific Notation

| Number | Number of Significant Digits | Scientific Notation | |---------------|------------------------------|--------------------------| | 0.00378 | 3 | 3.78 x 10^(-3) | | 3,780 | 4 | 3.78 x 10^(3) | | 10 | 1 | 1.0 x 10^(1) | | 0.130 | 3 | 1.30 x 10^(-1) | | 45,000,000 | 2 (if not specified) | 4.5 x 10^(7) |

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6. Completing the Calculations

a. \( 20.071 - (6.3 \times 1.222) \)

Step 1: Calculate \( 6.3 \times 1.222 \)

\[ 6.3 \times 1.222 = 7.6866 \]

The calculation has 2 significant digits (from 6.3), so we round:

\[ 7.6866 \approx 7.7 \quad (\text{rounded to 2 significant digits}) \]

Step 2: Perform the subtraction

\[ 20.071 - 7.7 = 12.371 \]

Since 7.7 has one decimal place, we round the final answer to one decimal place:

\[ 12.371 \approx 12.4 \]

Final answer for a:

\[ 12.4 \]

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b. \( (9.55 \times 10) - (8.476 \times 10^{80}) \)

This problem requires a careful consideration of the exponents since their magnitudes are vastly different.

Step 1: Perform the multiplication

\[ 9.55 \times 10 = 95.5 \] (The result has 3 significant digits due to 9.55.)

Step 2: Consider the second term

The first term (95.5) is significantly smaller than \( 8.476 \times 10^{80} \) (which is \( 847.6 \times 10^{77} \)).

When subtracting a very small number from a very large number, the small number can be generally ignored, leading to:

\[ (9.55 \times 10) - (8.476 \times 10^{80}) \approx -8.476 \times 10^{80} \]

Final answer for b:

\[ -8.476 \times 10^{80} \]

Summary of Answers:

4. Percent Error: 2.49%
5. Table: See completed table above
6. a: 12.4; b: -8.476 x 10^{80}