To solve these problems, we need to follow the rules of scientific notation. Scientific notation is written as a number between 1 and 10 multiplied by 10 raised to some power.
Here are the steps for each problem:
1.
(7 × 10⁸)(9 × 10⁶)
- Multiply the coefficients: \(7 \times 9 = 63\)
- Add the exponents: \(10^8 \times 10^6 = 10^{8+6} = 10^{14}\)
- Combine: \(63 \times 10^{14}\)
- Adjust to scientific notation: \(6.3 \times 10^{15}\)
2.
\(\frac{3 \times 10^4}{8 \times 10}\)
- Divide the coefficients: \(\frac{3}{8} = 0.375\)
- Subtract the exponents: \(10^4 \div 10 = 10^{4-1} = 10^3\)
- Combine: \(0.375 \times 10^3\)
- Adjust to scientific notation: \(3.75 \times 10^2\)
3.
\(\frac{4 \times 10^9}{5 \times 10^7}\)
- Divide the coefficients: \(\frac{4}{5} = 0.8\)
- Subtract the exponents: \(10^9 \div 10^7 = 10^{9-7} = 10^2\)
- Combine: \(0.8 \times 10^2\)
- Adjust to scientific notation: \(8 \times 10^1\)
4.
(2 × 10³)(3 × 10⁴)
- Multiply the coefficients: \(2 \times 3 = 6\)
- Add the exponents: \(10^3 \times 10^4 = 10^{3+4} = 10^7\)
- Combine: \(6 \times 10^7\)
5.
(3 × 10⁷)(9 × 10⁶)
- Multiply the coefficients: \(3 \times 9 = 27\)
- Add the exponents: \(10^7 \times 10^6 = 10^{7+6} = 10^{13}\)
- Combine: \(27 \times 10^{13}\)
- Adjust to scientific notation: \(2.7 \times 10^{14}\)
6.
\(\frac{4 \times 10^5}{16 \times 10^2}\)
- Divide the coefficients: \(\frac{4}{16} = 0.25\)
- Subtract the exponents: \(10^5 \div 10^2 = 10^{5-2} = 10^3\)
- Combine: \(0.25 \times 10^3\)
- Adjust to scientific notation: \(2.5 \times 10^2\)
7.
\(\frac{9 \times 10^5}{10 \times 10^3}\)
- Divide the coefficients: \(\frac{9}{10} = 0.9\)
- Subtract the exponents: \(10^5 \div 10^3 = 10^{5-3} = 10^2\)
- Combine: \(0.9 \times 10^2\)
- Adjust to scientific notation: \(9 \times 10^1\)
8.
(11 × 10⁴)(7 × 10²)
- Multiply the coefficients: \(11 \times 7 = 77\)
- Add the exponents: \(10^4 \times 10^2 = 10^{4+2} = 10^6\)
- Combine: \(77 \times 10^6\)
- Adjust to scientific notation: \(7.7 \times 10^7\)
Final Answer:
1. \(6.3 \times 10^{15}\)
2. \(3.75 \times 10^2\)
3. \(8 \times 10^1\)
4. \(6 \times 10^7\)
5. \(2.7 \times 10^{14}\)
6. \(2.5 \times 10^2\)
7. \(9 \times 10^1\)
8. \(7.7 \times 10^7\)
Parent Tip: Review the logic above to help your child master the concept of scientific notation multiplication and division worksheet.
