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Which of these time measurements is the smallest?

A. 0.02 seconds
B. 0.02 teraseconds
C. 2,500 milliseconds
D. 25,000 nanoseconds

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Answer :

Sure, for this question, we need to determine the smallest time measurement among the four options given. Let's proceed step-by-step with the conversions and comparisons:

1. Convert each measurement to seconds: This allows for an easy comparison.

- 0.02 seconds: This is already in seconds.

- 0.02 teraseconds: A terasecond is [tex]\(10^{12}\)[/tex] seconds. So, converting this:
[tex]\[ 0.02 \text{ teraseconds} = 0.02 \times 10^{12} \text{ seconds} = 20,000,000,000 \text{ seconds} \][/tex]

- 2,500 milliseconds: There are [tex]\(1,000\)[/tex] milliseconds in a second. So, converting this:
[tex]\[ 2,500 \text{ milliseconds} = 2,500 \div 1,000 \text{ seconds} = 2.5 \text{ seconds} \][/tex]

- 25,000 nanoseconds: There are [tex]\(1,000,000,000\)[/tex] (1 billion) nanoseconds in a second. So, converting this:
[tex]\[ 25,000 \text{ nanoseconds} = 25,000 \div 1,000,000,000 \text{ seconds} = 0.000025 \text{ seconds} \][/tex]

2. Compare all the converted time measurements:
- 0.02 seconds
- 20,000,000,000 seconds
- 2.5 seconds
- 0.000025 seconds

Clearly, by comparing these values:
[tex]\[ 20,000,000,000 \text{ seconds} > 2.5 \text{ seconds} > 0.02 \text{ seconds} > 0.000025 \text{ seconds} \][/tex]

3. Identifying the smallest time measurement:

From the comparisons above, the smallest time measurement is:
[tex]\[ 25,000 \text{ nanoseconds} = 0.000025 \text{ seconds} \][/tex]

So, the smallest time measurement among the given options is 25,000 nanoseconds.

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