To divide the two numbers \(1.95 \times 10^6\) and \(8.03 \times 10^{-8}\), we can follow these steps:
Step 1: Write the Division as a Fraction
We can express the division as a fraction:
\[ \frac{1.95 \times 10^6}{8.03 \times 10^{-8}} \]
Step 2: Separate the Coefficients and the Powers of 10
We can separate the coefficients and the powers of ten:
\[ \frac{1.95}{8.03} \times \frac{10^6}{10^{-8}} \]
Step 3: Simplify the Coefficients
Now, calculate \( \frac{1.95}{8.03} \):
\[ \frac{1.95}{8.03} \approx 0.243 (rounded to three decimal places) \]
Step 4: Simplify the Powers of 10
Now, simplify \( \frac{10^6}{10^{-8}} \) using the properties of exponents:
\[ 10^6 \div 10^{-8} = 10^{6 - (-8)} = 10^{6 + 8} = 10^{14} \]
Step 5: Combine the Results
Combine the simplified coefficient and the power of ten:
\[ 0.243 \times 10^{14} \]
Step 6: Express in Scientific Notation
To express \(0.243 \times 10^{14}\) in proper scientific notation, we need to adjust it to be in the form \(a \times 10^b\), where \(1 \leq a < 10\):
\[ 0.243 \times 10^{14} = 2.43 \times 10^{13} \]
So, the final answer for the division of \(1.95 \times 10^6\) and \(8.03 \times 10^{-8}\) is:
\[ \frac{1.95 \times 10^6}{8.03 \times 10^{-8}} = 2.43 \times 10^{13} \]
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