Question

1. \\((3 \times 10^{-6})(2.6 \times 10^{4})\\)

1. \\(\frac{(6.10 \times 10^{4})(7.002 \times 10^{-6})}{9.80 \times 10^{4}}\\)

\\(\frac{40,000(0.29)}{0.057(160,000)}\\)

Explanation:

Problem 3:

Step1: Separate coefficients and powers

$(3 \times 2.6) \times (10^{-6} \times 10^{4})$

Step2: Multiply coefficients and powers

$7.8 \times 10^{-6+4} = 7.8 \times 10^{-2}$

Problem 8:

Step1: Separate coefficients and powers

$\frac{6.10 \times 7.002}{9.80} \times \frac{10^{4} \times 10^{-6}}{10^{4}}$

Step2: Calculate coefficient part

$\frac{42.7122}{9.80} \approx 4.3584$

Step3: Calculate power part

$10^{4+(-6)-4} = 10^{-6}$

Step4: Combine results

$4.3584 \times 10^{-6} \approx 4.36 \times 10^{-6}$

Problem 3 (bottom):

Step1: Calculate numerator and denominator

$\frac{40000 \times 0.29}{0.057 \times 160000} = \frac{11600}{9120}$

Step2: Simplify the fraction

$\frac{11600}{9120} \approx 1.27$

Answer:

1. $7.8 \times 10^{-2}$
2. $4.36 \times 10^{-6}$
3. $\approx 1.27$