Sure, let's break down the calculation step-by-step, showing the answer from a calculator, determining significant digits, and identifying how many significant digits are in the original numbers.
Step 1: Perform the Division
Using a calculator, we perform the division:
\[ \frac{3.76}{1.62} = 2.31481481481 \]
Step 2: Identify the Significant Figures
Now, we need to identify the number of significant digits in both the numerator (3.76) and the denominator (1.62).
3.76:
- Both digits "3," "7," and "6" are significant.
- Total significant digits in 3.76 = 3
1.62:
- Both digits "1," "6," and "2" are significant.
- Total significant digits in 1.62 = 3
Step 3: Determine the Result's Significant Digits
In division operations, the result should be reported with the same number of significant digits as the number with the least significant digits used in the calculation.
Here, both 3.76 and 1.62 have 3 significant digits. Therefore, the result must also be rounded to 3 significant digits.
Step 4: Round the Result
The full result from the calculator is:
\[ 2.31481481481 \]
To round it to 3 significant digits:
- The first three significant digits are "2," "3," and "1."
- The digit following "1" is "4," which does not round "1" up. Thus, we keep "1" as is.
So, rounding gives us:
\[ 2.31 \]
Final Results
- Calculator answer: 2.31481481481
- Significant digits answer: 2.31
- Number of significant digits in the final answer: 3
Summary
- \( \frac{3.76}{1.62} = 2.31 \) (rounded to three significant digits).