Which is the correct 'power of 10' expression of $10,000?$
A. $10^5$
B. $10^2$
C. $10^4$
D. $10^{-4}$
Answer (2)
Calculate each option: 1 0 5 = 100 , 000 , 1 0 2 = 100 , 1 0 4 = 10 , 000 , 1 0 − 4 = 0.0001 .
Compare the results to 10,000.
Identify the correct option: 1 0 4 = 10 , 000 .
The correct 'power of 10' expression of 10,000 is 1 0 4 .
Explanation
Understanding the Problem We need to find the correct power of 10 that equals 10,000. The options are 1 0 5 , 1 0 2 , 1 0 4 , and 1 0 − 4 .
Calculating the Options Let's calculate the value of each option:
1 0 5 = 10 × 10 × 10 × 10 × 10 = 100 , 000
1 0 2 = 10 × 10 = 100
1 0 4 = 10 × 10 × 10 × 10 = 10 , 000
1 0 − 4 = 1 0 4 1 = 10 , 000 1 = 0.0001
Finding the Correct Option Comparing the calculated values with 10,000, we find that 1 0 4 = 10 , 000 . Therefore, the correct power of 10 expression for 10,000 is 1 0 4 .
Final Answer The correct answer is 1 0 4 .
Examples
Understanding powers of 10 is crucial in various real-life scenarios. For instance, in computer science, data storage is often measured in powers of 2 (which are closely related to powers of 10). A kilobyte (KB) is approximately 1 0 3 bytes, a megabyte (MB) is approximately 1 0 6 bytes, and a gigabyte (GB) is approximately 1 0 9 bytes. Similarly, in scientific notation, very large or very small numbers are expressed using powers of 10 to make them easier to work with. For example, the distance to a star might be 1.5 × 1 0 15 meters.
The correct 'power of 10' expression for 10,000 is 1 0 4 . This is determined by calculating each option and comparing them to 10,000. Thus, the answer is option C: 1 0 4 .
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