Divide, expressing the quotient in scientific notation.
$\frac{2.4 \times 10^8}{5 \times 10^{-6}}$
Answer (1)
Divide the coefficients: 5 2.4 = 0.48 .
Divide the powers of 10: 1 0 − 6 1 0 8 = 1 0 14 .
Combine the results: 0.48 × 1 0 14 .
Express in scientific notation: 4.8 × 1 0 13 .
Explanation
Understanding the problem We are asked to divide two numbers expressed in scientific notation and express the result in scientific notation. The given expression is: 5 × 1 0 − 6 2.4 × 1 0 8
Dividing coefficients and powers of 10 To divide numbers in scientific notation, we divide the coefficients and divide the powers of 10. So, we have: 5 2.4 × 1 0 − 6 1 0 8
Dividing the coefficients First, let's divide the coefficients: 5 2.4 = 0.48
Dividing the powers of 10 Next, let's divide the powers of 10: 1 0 − 6 1 0 8 = 1 0 8 − ( − 6 ) = 1 0 8 + 6 = 1 0 14
Combining the results Now, combine the results: 0.48 × 1 0 14
Expressing in scientific notation To express this in proper scientific notation, we need to write 0.48 as 4.8 × 1 0 − 1 . So we have: 4.8 × 1 0 − 1 × 1 0 14 = 4.8 × 1 0 − 1 + 14 = 4.8 × 1 0 13
Final answer Therefore, the final answer in scientific notation is: 4.8 × 1 0 13
Examples
Scientific notation is used in many fields, such as astronomy, to represent very large or very small numbers. For example, the distance to a star might be 4.8 × 1 0 13 kilometers. Understanding how to divide numbers in scientific notation helps astronomers calculate ratios of distances, brightness, and other properties of celestial objects. This is also useful in fields like chemistry and physics when dealing with atomic and subatomic particles.
