Express in scientific notation:
[tex]\frac{9 \times 10^9}{4.5 \times 10^1}=\qquad[/tex]
A. [tex]2.0 \times 10^8[/tex]
B. [tex]2.0^8[/tex]
C. [tex]2 \times 10^8[/tex]
Answer (1)
Divide the coefficients: 4.5 9 = 2 .
Divide the powers of 10: 1 0 1 1 0 9 = 1 0 8 .
Combine the results: 2 × 1 0 8 .
The correct answer is: 2 × 1 0 8 .
Explanation
Understanding the Problem We are asked to express the given expression in scientific notation and choose the correct answer from the provided options. The expression is: 4.5 × 1 0 1 9 × 1 0 9 The options are: 2.0 × 1 0 8 , 2. 0 8 , 2 × 1 0 8
Dividing the Coefficients First, we divide the coefficients: 4.5 9 = 2
Dividing the Powers of 10 Next, we divide the powers of 10: 1 0 1 1 0 9 = 1 0 9 − 1 = 1 0 8
Combining the Results Now, we combine the results: 2 × 1 0 8
Choosing the Correct Answer Comparing our result with the given options, we see that 2 × 1 0 8 is the correct answer. Note that 2.0 × 1 0 8 is the same as 2 × 1 0 8 , but the question asks for the answer with the proper number.
Final Answer Therefore, the expression in scientific notation is: 2 × 1 0 8
Examples
Scientific notation is used in many fields, such as physics and astronomy, to represent very large or very small numbers. For example, the distance to the sun is approximately 1.5 × 1 0 11 meters, and the size of an atom is approximately 1 × 1 0 − 10 meters. Using scientific notation makes it easier to work with these numbers.
