Question

1. \\((2.013 \times 10^{6})(4.2 \times 10^{-11})\\)\
2. \\(\frac{8.512 \times 10^{8}}{3.4012 \times 10^{5}}\\)\
3. \\(\frac{2.42 \times 10^{5}}{1.21 \times 10^{-5}}\\)\
4. \\(\frac{780,000,000.01(0.00071)}{0.0000005}\\)

Explanation:

Problem 1:

Step1: Separate coefficients and powers

$(2.013 \times 4.2) \times (10^{6} \times 10^{-11})$

Step2: Multiply coefficients

$2.013 \times 4.2 = 8.4546$

Step3: Multiply powers of 10

$10^{6 + (-11)} = 10^{-5}$

Step4: Combine results

$8.4546 \times 10^{-5}$

Problem 4:

Step1: Separate coefficients and powers

$\frac{8.512}{3.4012} \times \frac{10^{8}}{10^{5}}$

Step2: Divide coefficients

$\frac{8.512}{3.4012} \approx 2.503$

Step3: Divide powers of 10

$10^{8 - 5} = 10^{3}$

Step4: Combine results

$2.503 \times 10^{3}$

Problem 6:

Step1: Separate coefficients and powers

$\frac{2.42}{1.21} \times \frac{10^{5}}{10^{-5}}$

Step2: Divide coefficients

$\frac{2.42}{1.21} = 2$

Step3: Divide powers of 10

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

Step4: Combine results

$2 \times 10^{10}$

Problem 9:

Step1: Convert to scientific notation

$\frac{(7.8000000001 \times 10^{8}) \times (7.1 \times 10^{-4})}{5 \times 10^{-6}}$

Step2: Multiply numerator terms

$(7.8000000001 \times 7.1) \times (10^{8} \times 10^{-4}) = 55.38000000071 \times 10^{4}$

Step3: Divide by denominator

$\frac{55.38000000071}{5} \times \frac{10^{4}}{10^{-6}}$

Step4: Calculate coefficient and power

$11.076000000142 \times 10^{10} = 1.1076000000142 \times 10^{11}$

Answer:

1. $8.4546 \times 10^{-5}$
2. $2.503 \times 10^{3}$
3. $2 \times 10^{10}$
4. $1.1076000000142 \times 10^{11}$