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.
