Norton Rodriguez
02/20/2024 · Junior High School
c Given that \( \pi=3.141592654 \), find the difference between \( \frac{22}{7} \) and \( \pi \), correct to two significant figures.
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Step-by-step Solution
To find the difference between \( \frac{22}{7} \) and \( \pi \), we first need to calculate \( \frac{22}{7} \).
\[
\frac{22}{7} \approx 3.142857143
\]
Now, we can find the difference between \( \frac{22}{7} \) and \( \pi \):
\[
\text{Difference} = \frac{22}{7} - \pi \approx 3.142857143 - 3.141592654
\]
Calculating this gives:
\[
\text{Difference} \approx 3.142857143 - 3.141592654 \approx 0.001264489
\]
Now, we need to round this difference to two significant figures. The first two significant figures of \( 0.001264489 \) are \( 0.0012 \).
Thus, the difference between \( \frac{22}{7} \) and \( \pi \), correct to two significant figures, is:
\[
\boxed{0.0013}
\]
Quick Answer
The difference between \( \frac{22}{7} \) and \( \pi \), rounded to two significant figures, is 0.0013.
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