Perform the following operation and express the answer in proper scientific notation.
$\frac{5.5 \times 10^7}{3.25 \times 10^{-3}}=[?] \times 10^{[?]}$
Enter the coefficient in the green box and the exponent in the yellow one.
Coefficient (green)
Answer (2)
The result of the division 3.25 × 1 0 − 3 5.5 × 1 0 7 is 1.6923076923076923 × 1 0 10 . The coefficient is approximately 1.6923 and the exponent is 10. This result is already in proper scientific notation.
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Divide the coefficients: 3.25 5.5 = 1.6923076923076923 .
Divide the powers of 10: 1 0 − 3 1 0 7 = 1 0 10 .
Combine the results: 1.6923076923076923 × 1 0 10 .
Express the answer in scientific notation: 1.6923076923076923 × 1 0 10 .
Explanation
Understanding the Problem We are asked to perform the division 3.25 × 1 0 − 3 5.5 × 1 0 7 and express the answer in scientific notation. Scientific notation requires the result to be in the form a × 1 0 b , where 1 ≤ a < 10 and b is an integer.
Dividing the Coefficients First, we divide the coefficients: 3.25 5.5 = 1.6923076923076923
Dividing the Powers of 10 Next, we divide the powers of 10: 1 0 − 3 1 0 7 = 1 0 7 − ( − 3 ) = 1 0 7 + 3 = 1 0 10
Combining the Results Now, we combine the results: 1.6923076923076923 × 1 0 10 Since 1 ≤ 1.6923076923076923 < 10 , the result is already in proper scientific notation.
Final Answer Therefore, the final answer in scientific notation is 1.6923076923076923 × 1 0 10 .
Examples
Scientific notation is extremely useful in various fields like physics, astronomy, and engineering where dealing with very large or very small numbers is common. For instance, the distance to the Andromeda galaxy is approximately 2.5 × 1 0 22 meters, and the size of an atom is about 1 × 1 0 − 10 meters. Using scientific notation makes these numbers easier to handle and compare.
