Which of the following is the same as $2.3 \times 10^3$?
A. 023
B. 2,300
C. 230
D. .23
Answer (2)
We are given the expression 2.3" , " t im es 1 0 3 .
We calculate 1 0 3 = 1000 .
We multiply 2.3" , " t im es 1000 = 2300 .
The correct answer is 2300 .
Explanation
Understanding the problem We are asked to find the value of 2.3" , " t im es 1 0 3 and determine which of the given options is equivalent to it. The expression 1 0 3 means 10 raised to the power of 3, which is equal to 10" , " t im es 10" , " t im es 10 = 1000 .
Performing the calculation Now, we need to multiply 2.3 by 1000. Multiplying a number by 1000 is the same as moving the decimal point three places to the right. So, 2.3" , " t im es 1000 = 2300 .
Finding the correct option Comparing our result, 2300, with the given options, we see that option B, which is 2,300, matches our result.
Final Answer Therefore, the correct answer is B. 2,300.
Examples
Understanding scientific notation is useful in many real-world scenarios. For example, in physics, the speed of light is approximately 3" , " t im es 1 0 8 meters per second. This notation allows us to express very large or very small numbers in a compact and manageable form. Similarly, in computer science, the storage capacity of a hard drive might be expressed in terabytes (TB), where 1 TB is approximately 1 0 12 bytes. Using scientific notation helps to simplify these large numbers and make them easier to work with.
The expression 2.3 × 1 0 3 evaluates to 2300. The correct answer from the options given is B: 2,300. This result comes from multiplying 2.3 by 1000, which is what 1 0 3 represents.
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