Question

dividing scientific notation

1. $(3 \times 10^{-2}) \div (0.3 \times 10^{5})$
2. $(9.660 \times 10^{7}) \div (1.650 \times 10^{4})$
3. $(7.4 \times 10^{9}) \div (1.28 \times 10^{4})$
4. $(1.5 \times 10^{-4}) \div (6 \times 10^{2})$
5. $(8.1 \times 10^{-3}) \div (9.0 \times 10^{2})$
6. $(1.18 \times 10^{-4}) \div (3 \times 10^{4})$
7. $(6 \times 10^{-3}) \div (8.08 \times 10^{-2})$
8. $(4.1 \times 10^{4}) \div (1.28 \times 10^{-5})$
9. $(5.5 \times 10^{-1}) \div (5.3 \times 10^{2})$
10. $(1.91 \times 10^{3}) \div (5 \times 10^{-4})$

Explanation:

Step1: Split coefficients and powers

For $\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}$, apply to each problem.
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Problem 1: $(3 \times 10^7) \div (1.3 \times 10^5)$

Step1: Divide coefficients

$\frac{3}{1.3} \approx 2.31$

Step2: Subtract exponents

$10^{7-5} = 10^2$

Step3: Combine results

$2.31 \times 10^2$

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Problem 2: $(9.60 \times 10^7) \div (1.60 \times 10^4)$

Step1: Divide coefficients

$\frac{9.60}{1.60} = 6$

Step2: Subtract exponents

$10^{7-4} = 10^3$

Step3: Combine results

$6 \times 10^3$

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Problem 3: $(1.4 \times 10^6) \div (1.28 \times 10^4)$

Step1: Divide coefficients

$\frac{1.4}{1.28} \approx 1.09$

Step2: Subtract exponents

$10^{6-4} = 10^2$

Step3: Combine results

$1.09 \times 10^2$

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Problem 4: $(1.5 \times 10^9) \div (5 \times 10^7)$

Step1: Divide coefficients

$\frac{1.5}{5} = 0.3 = 3 \times 10^{-1}$

Step2: Subtract exponents

$10^{9-7} = 10^2$

Step3: Combine results

$3 \times 10^{-1} \times 10^2 = 3 \times 10^{1}$

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Problem 5: $(8.1 \times 10^{-2}) \div (9.0 \times 10^2)$

Step1: Divide coefficients

$\frac{8.1}{9.0} = 0.9 = 9 \times 10^{-1}$

Step2: Subtract exponents

$10^{-2-2} = 10^{-4}$

Step3: Combine results

$9 \times 10^{-1} \times 10^{-4} = 9 \times 10^{-5}$

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Problem 6: $(1.18 \times 10^{-4}) \div (3 \times 10^3)$

Step1: Divide coefficients

$\frac{1.18}{3} \approx 0.39 = 3.9 \times 10^{-1}$

Step2: Subtract exponents

$10^{-4-3} = 10^{-7}$

Step3: Combine results

$3.9 \times 10^{-1} \times 10^{-7} = 3.9 \times 10^{-8}$

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Problem 7: $(6 \times 10^{-3}) \div (8.08 \times 10^{-2})$

Step1: Divide coefficients

$\frac{6}{8.08} \approx 0.74 = 7.4 \times 10^{-1}$

Step2: Subtract exponents

$10^{-3-(-2)} = 10^{-1}$

Step3: Combine results

$7.4 \times 10^{-1} \times 10^{-1} = 7.4 \times 10^{-2}$

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Problem 8: $(4.1 \times 10^4) \div (1.28 \times 10^{-5})$

Step1: Divide coefficients

$\frac{4.1}{1.28} \approx 3.20$

Step2: Subtract exponents

$10^{4-(-5)} = 10^9$

Step3: Combine results

$3.20 \times 10^9$

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Problem 9: $(5.5 \times 10^{-7}) \div (5.3 \times 10^2)$

Step1: Divide coefficients

$\frac{5.5}{5.3} \approx 1.04$

Step2: Subtract exponents

$10^{-7-2} = 10^{-9}$

Step3: Combine results

$1.04 \times 10^{-9}$

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Problem 10: $(1.91 \times 10^3) \div (5 \times 10^{-4})$

Step1: Divide coefficients

$\frac{1.91}{5} = 0.382 = 3.82 \times 10^{-1}$

Step2: Subtract exponents

$10^{3-(-4)} = 10^7$

Step3: Combine results

$3.82 \times 10^{-1} \times 10^7 = 3.82 \times 10^6$

Answer:

1. $2.31 \times 10^2$
2. $6 \times 10^3$
3. $1.09 \times 10^2$
4. $3 \times 10^1$
5. $9 \times 10^{-5}$
6. $3.9 \times 10^{-8}$
7. $7.4 \times 10^{-2}$
8. $3.20 \times 10^9$
9. $1.04 \times 10^{-9}$
10. $3.82 \times 10^6$