Which conversion factor(s) would be needed to convert nanoseconds to milliseconds?
a. 1 s = 1,000,000,000 ns and 1 s = 1,000 ms
b. 1 s = 1,000 ms
c. 1 s = 1,000,000,000 ns
d. 1ns = 1,000 ms
The Correct Answer and Explanation is :
The correct answer is: a. 1 s = 1,000,000,000 ns and 1 s = 1,000 ms
Explanation:
To convert from nanoseconds (ns) to milliseconds (ms), we must first understand the relationships between these units and seconds (s):
- Nanoseconds to seconds:
[
1 \, \text{s} = 1,000,000,000 \, \text{ns} \quad \text{(conversion factor #1)}.
] This means there are (10^9) nanoseconds in one second. - Seconds to milliseconds:
[
1 \, \text{s} = 1,000 \, \text{ms} \quad \text{(conversion factor #2)}.
] This means there are (10^3) milliseconds in one second.
To convert from nanoseconds to milliseconds, we combine these two steps:
Step-by-step Conversion:
- Convert nanoseconds to seconds:
Use (1 \, \text{s} = 1,000,000,000 \, \text{ns}):
[
\text{time in seconds} = \frac{\text{time in nanoseconds}}{1,000,000,000}.
] - Convert seconds to milliseconds:
Use (1 \, \text{s} = 1,000 \, \text{ms}):
[
\text{time in milliseconds} = \text{time in seconds} \times 1,000.
]
Combined Conversion:
The two steps can be combined into a single equation:
[
\text{time in milliseconds} = \frac{\text{time in nanoseconds}}{1,000,000}.
]
This shows that both 1 s = 1,000,000,000 ns and 1 s = 1,000 ms are required for the conversion.
Why the other options are incorrect:
- b. 1 s = 1,000 ms: Insufficient for conversion without ns to s.
- c. 1 s = 1,000,000,000 ns: Insufficient for conversion without ms to s.
- d. 1 ns = 1,000 ms: Incorrect; 1 ns equals (10^{-6}) ms.