I'll solve each problem step by step, working with scientific notation and rounding to the nearest tenth.
Let me work through all 8 problems:
Problem 1 (top): (6.5 × 10²)(4.13 × 10⁴)
- Multiply coefficients: 6.5 × 4.13 = 26.845
- Add exponents: 10² × 10⁴ = 10⁶
- Result: 26.845 × 10⁶
- Convert to proper scientific notation: 2.6845 × 10
- Round to nearest tenth:
2.7 × 10⁷
Problem 2 (top right): (9.3 × 10⁷) ÷ 23,000
- Convert 23,000 to scientific notation: 2.3 × 10⁴
- Divide coefficients: 9.3 ÷ 2.3 = 4.043...
- Subtract exponents: 10⁷ ÷ 10⁴ = 10³
- Result: 4.043 × 10³
- Round to nearest tenth:
4.0 × 10³
Problem 3 (bottom right): (6.1 × 10⁻⁵)(7.2 × 10⁶)
- Multiply coefficients: 6.1 × 7.2 = 43.92
- Add exponents: 10⁻⁵ × 10⁶ = 10¹
- Result: 43.92 × 10¹
- Convert to proper scientific notation: 4.392 × 10²
- Round to nearest tenth:
4.4 × 10²
Problem 4 (bottom): (3.5 × 10²)(1.1 × 10)
- Multiply coefficients: 3.5 × 1.1 = 3.85
- Add exponents: 10² × 10⁴ = 10⁶
- Result: 3.85 × 10⁶
- Round to nearest tenth:
3.9 × 10⁶
Problem 5 (bottom left): (5.2 × 10⁶) ÷ (1.1 × 10³)
- Divide coefficients: 5.2 ÷ 1.1 = 4.727...
- Subtract exponents: 10⁶ ÷ 10³ = 10³
- Result: 4.727 × 10³
- Round to nearest tenth:
4.7 × 10³
Problem 6 (top left): (6.2 × 10³)(5.6 × 10⁵)
- Multiply coefficients: 6.2 × 5.6 = 34.72
- Add exponents: 10³ × 10⁵ = 10⁸
- Result: 34.72 × 10⁸
- Convert to proper scientific notation: 3.472 × 10⁹
- Round to nearest tenth:
3.5 × 10⁹
Problem 7 (center): (5.1 × 10³) × 520,000
- Convert 520,000 to scientific notation: 5.2 × 10
- Multiply coefficients: 5.1 × 5.2 = 26.52
- Add exponents: 10³ × 10⁵ = 10⁸
- Result: 26.52 × 10⁸
- Convert to proper scientific notation: 2.652 × 10⁹
- Round to nearest tenth:
2.7 × 10⁹
Final Answer:
1. Top: 2.7 × 10⁷
2. Top right: 4.0 × 10³
3. Bottom right: 4.4 × 10²
4. Bottom: 3.9 × 10⁶
5. Bottom left: 4.7 × 10³
6. Top left: 3.5 × 10⁹
7. Center: 2.7 × 10⁹
Parent Tip: Review the logic above to help your child master the concept of maths puzzles printable year 8.
