Express in scientific notation: [tex]\frac{1.24 \times 10^6}{6.2 \times 10^{-3}}=[/tex]
Answer (2)
Divide the coefficients: 6.2 1.24 = 0.2 .
Divide the powers of 10: 1 0 − 3 1 0 6 = 1 0 9 .
Combine the results: 0.2 × 1 0 9 = 2.0 × 1 0 8 .
Express the final answer with 2 significant figures: 2.0 × 1 0 8 .
Explanation
Understanding the Problem We are asked to express the result of the division 6.2 × 1 0 − 3 1.24 × 1 0 6 in scientific notation, paying attention to significant figures. The numerator has 3 significant figures (1.24), and the denominator has 2 significant figures (6.2). Therefore, the final answer should be expressed with 2 significant figures.
Dividing the Coefficients First, we divide the coefficients: 6.2 1.24 = 0.2 .
Dividing the Powers of 10 Next, we divide the powers of 10: 1 0 − 3 1 0 6 = 1 0 6 − ( − 3 ) = 1 0 6 + 3 = 1 0 9 .
Expressing in Scientific Notation Combining these results, we get 0.2 × 1 0 9 . However, this is not in proper scientific notation, which requires the coefficient to be between 1 and 10. So, we rewrite this as 2.0 × 1 0 8 . Since we need to express the answer with 2 significant figures, we write 2.0 instead of 2.
Final Answer Comparing our result with the given options, we see that the correct answer is 2.0 × 1 0 8 .
Examples
Scientific notation is extremely useful in fields like astronomy and physics, where dealing with very large or very small numbers is common. For example, the distance to the nearest star (other than the Sun) is approximately 4.0 × 1 0 16 meters. Similarly, the mass of an electron is approximately 9.11 × 1 0 − 31 kg. Using scientific notation makes these numbers easier to write, compare, and perform calculations with.
To divide 1.24 × 1 0 6 by 6.2 × 1 0 − 3 , divide the coefficients and the powers of ten separately. The result is 2.0 × 1 0 8 in proper scientific notation. This maintains significant figures based on the inputs used.
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