This worksheet provides practice problems for students to master significant figures, rounding, scientific notation, and metric conversions.

Problem Analysis and Solution

The worksheet provided involves several tasks related to scientific measurements, significant figures, unit conversions, and exponent rules. Let's solve each part step by step.

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#### Task 1: Determine the number of significant figures in each of the following values

1. 7.42
- All non-zero digits are significant.
- Significant figures: 3

2. 0.0028
- Leading zeros are not significant.
- Non-zero digits (2 and 8) are significant.
- Significant figures: 2

3. 46
- All non-zero digits are significant.
- Significant figures: 2

4. 1.25 × 10⁵
- In scientific notation, only the digits before the "× 10ⁿ" are considered.
- Significant figures: 3

5. 0.00014
- Leading zeros are not significant.
- Non-zero digits (1 and 4) are significant.
- Significant figures: 2

Answers for Task 1:
- 7.42: 3
- 0.0028: 2
- 46: 2
- 1.25 × 10⁵: 3
- 0.00014: 2

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#### Task 2: Round each of the following to the nearest:
- 100th (two decimal places)
- 10th (one decimal place)
- 1st (whole number)

1. 3.2645
- Nearest 100th: 3.26
- Nearest 10th: 3.3
- Nearest 1st: 3

2. 0.05736
- Nearest 100th: 0.06
- Nearest 10th: 0.1
- Nearest 1st: 0

3. 821.4578
- Nearest 100th: 821.46
- Nearest 10th: 821.5
- Nearest 1st: 821

4. 1.234567
- Nearest 100th: 1.23
- Nearest 10th: 1.2
- Nearest 1st: 1

5. 3.249567
- Nearest 100th: 3.25
- Nearest 10th: 3.2
- Nearest 1st: 3

Answers for Task 2:
- 3.2645: 3.26, 3.3, 3
- 0.05736: 0.06, 0.1, 0
- 821.4578: 821.46, 821.5, 821
- 1.234567: 1.23, 1.2, 1
- 3.249567: 3.25, 3.2, 3

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#### Task 3: Simplify the following expressions using the basics of exponents

1. (3.2 × 10³) × (9.2 × 10²)
- Multiply the coefficients: \(3.2 \times 9.2 = 29.44\)
- Add the exponents: \(10^3 \times 10^2 = 10^{3+2} = 10^5\)
- Result: \(29.44 \times 10^5\)
- Convert to proper scientific notation: \(2.944 \times 10^6\)

2. (3.2 × 10⁻³) ÷ (9.2 × 10²)
- Divide the coefficients: \(3.2 ÷ 9.2 \approx 0.3478\)
- Subtract the exponents: \(10^{-3} ÷ 10^2 = 10^{-3-2} = 10^{-5}\)
- Result: \(0.3478 \times 10^{-5}\)
- Convert to proper scientific notation: \(3.478 \times 10^{-6}\)

3. (3.2 × 10³)²
- Square the coefficient: \(3.2^2 = 10.24\)
- Multiply the exponents: \((10^3)^2 = 10^{3 \times 2} = 10^6\)
- Result: \(10.24 \times 10^6\)
- Convert to proper scientific notation: \(1.024 \times 10^7\)

4. (3.2 × 10³) ÷ (9.2 × 10⁻²)
- Divide the coefficients: \(3.2 ÷ 9.2 \approx 0.3478\)
- Subtract the exponents: \(10^3 ÷ 10^{-2} = 10^{3 - (-2)} = 10^5\)
- Result: \(0.3478 \times 10^5\)
- Convert to proper scientific notation: \(3.478 \times 10^4\)

Answers for Task 3:
- (3.2 × 10³) × (9.2 × 10²): 2.944 × 10⁶
- (3.2 × 10⁻³) ÷ (9.2 × 10²): 3.478 × 10⁻⁶
- (3.2 × 10³)²: 1.024 × 10⁷
- (3.2 × 10³) ÷ (9.2 × 10⁻²): 3.478 × 10⁴

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#### Task 4: Convert the following measurements, check all that are correct, and round each of the following as necessary

1. 15 Meters to Millimeters
- 1 meter = 1000 millimeters
- \(15 \text{ meters} = 15 \times 1000 = 15000 \text{ millimeters}\)
- Correct conversion: 15000 mm

2. 22 Feet to Millimeters
- 1 foot = 304.8 millimeters
- \(22 \text{ feet} = 22 \times 304.8 = 6705.6 \text{ millimeters}\)
- Correct conversion: 6705.6 mm

3. 54 Feet to Yards
- 1 yard = 3 feet
- \(54 \text{ feet} = 54 ÷ 3 = 18 \text{ yards}\)
- Correct conversion: 18 yd

4. 36 cm to in
- 1 inch = 2.54 cm
- \(36 \text{ cm} = 36 ÷ 2.54 \approx 14.17 \text{ inches}\)
- Correct conversion: 14.17 in

5. 235.2 km to miles
- 1 mile ≈ 1.60934 km
- \(235.2 \text{ km} = 235.2 ÷ 1.60934 \approx 146.15 \text{ miles}\)
- Correct conversion: 146.15 mi

6. 65 miles per hour to meters per second
- 1 mile = 1609.34 meters
- 1 hour = 3600 seconds
- \(65 \text{ mph} = 65 \times \frac{1609.34}{3600} \approx 29.06 \text{ m/s}\)
- Correct conversion: 29.06 m/s

7. 18 kg to lb
- 1 kilogram ≈ 2.20462 pounds
- \(18 \text{ kg} = 18 \times 2.20462 \approx 39.68 \text{ pounds}\)
- Correct conversion: 39.68 lb

Answers for Task 4:
- 15 Meters to Millimeters: 15000 mm
- 22 Feet to Millimeters: 6705.6 mm
- 54 Feet to Yards: 18 yd
- 36 cm to in: 14.17 in
- 235.2 km to miles: 146.15 mi
- 65 miles per hour to meters per second: 29.06 m/s
- 18 kg to lb: 39.68 lb

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Task 1: } 3, 2, 2, 3, 2 \\
\text{Task 2: } 3.26, 3.3, 3; \, 0.06, 0.1, 0; \, 821.46, 821.5, 821; \, 1.23, 1.2, 1; \, 3.25, 3.2, 3 \\
\text{Task 3: } 2.944 \times 10^6, 3.478 \times 10^{-6}, 1.024 \times 10^7, 3.478 \times 10^4 \\
\text{Task 4: } 15000 \text{ mm}, 6705.6 \text{ mm}, 18 \text{ yd}, 14.17 \text{ in}, 146.15 \text{ mi}, 29.06 \text{ m/s}, 39.68 \text{ lb}
\end{array}
}
\]