Perform the following operation and express the answer in proper scientific notation:
[tex]\frac{9.0 \times 10^{-5}}{2.0 \times 10^{-8}}=[/tex]
Enter the coefficient in the green box and the exponent in the yellow one.
Coefficient (green)
Exponent (yellow)
Answer (2)
The expression 2.0 × 1 0 − 8 9.0 × 1 0 − 5 simplifies to 4.5 × 1 0 3 . Thus, the coefficient is 4.5 and the exponent is 3.
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Divide the coefficients: 2.0 9.0 = 4.5 .
Divide the powers of 10: 1 0 − 8 1 0 − 5 = 1 0 3 .
Combine the results: 4.5 × 1 0 3 .
The coefficient is 4.5 and the exponent is 3, so the answer is 4.5 and 3 .
Explanation
Understanding the Problem We are asked to divide two numbers expressed in scientific notation and express the result in proper scientific notation. The expression is 2.0 × 1 0 − 8 9.0 × 1 0 − 5 . The result should be expressed as a × 1 0 b where 1 ≤ a < 10 and b is an integer.
Dividing the Coefficients First, we divide the coefficients: 2.0 9.0 = 4.5
Dividing the Powers of 10 Next, we divide the powers of 10: 1 0 − 8 1 0 − 5 = 1 0 − 5 − ( − 8 ) = 1 0 − 5 + 8 = 1 0 3
Combining the Results Now, we combine the results: 2.0 × 1 0 − 8 9.0 × 1 0 − 5 = 2.0 9.0 × 1 0 − 8 1 0 − 5 = 4.5 × 1 0 3
Final Answer The result is already in proper scientific notation, so the coefficient is 4.5 and the exponent is 3.
Examples
Scientific notation is extremely useful in various fields like physics, astronomy, and chemistry, where dealing with very large or very small numbers is common. For instance, the speed of light is approximately 3.0 × 1 0 8 meters per second, and the size of an atom is around 1.0 × 1 0 − 10 meters. Using scientific notation makes these numbers easier to handle and compare.
