To solve the division of \(7.895\) by \(34\) and assess the significance of the digits in the answer, we will go through the process step-by-step.
Step 1: Perform the Calculation
Using a calculator: \[ \frac{7.895}{34} \approx 0.2320794117647059 \]
Step 2: Determine Significant Digits
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Identify Significant Digits in the Numbers:
- For \(7.895\):
- All non-zero digits (7, 8, 9, 5) are significant.
- Total significant digits = 4.
- For \(34\):
- Both digits (3 and 4) are significant.
- Total significant digits = 2.
- For \(7.895\):
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Rules for Significant Figures in Division:
- In division, the result should have the same number of significant figures as the number with the least significant figures.
- Here, \(34\) has 2 significant digits, which is the smaller value compared to \(7.895\) with 4 significant digits.
Step 3: Round the Result
Since the number with the least significant digits (the divisor \(34\)) has 2 significant figures, we need to round our answer \(0.2320794117647059\) to 2 significant figures.
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Starting with \(0.2320794117647059\), we identify the first two significant figures:
- First significant digit: 2
- Second significant digit: 3
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Considering the next digit (which is 2), we keep the first two significant digits as \(0.23\) because it does not round up.
Final Answer Summary
- Calculator Answer: \(0.2320794117647059\)
- Rounded Answer with Significant Figures: \(0.23\)
- Number of Significant Digits in the Final Answer: 2
Thus, the result of \(7.895 / 34\) rounded to the correct number of significant digits is: \[ \boxed{0.23} \]