To solve the problem \( 920.7 \div 4.32 \) and express the answer with the correct number of significant digits, we will break the process down into clear steps.
Step 1: Perform the Calculation
Using a calculator:
\[ 920.7 \div 4.32 \approx 213.54 \]
Step 2: Determine Significant Digits
Now we will identify the number of significant digits in each of the numbers involved in the calculation:
-
For 920.7:
- This is a decimal number and all non-zero digits are significant. The digit '9', '2', '0', and '7' are all significant.
- Significant digits in 920.7 = 4
-
For 4.32:
- This is also a decimal number. All non-zero digits are significant, and the zero is significant because it is between non-zero digits.
- Significant digits in 4.32 = 3
Step 3: Apply the Rule for Significant Figures in Division
When dividing, the result should have the same number of significant digits as the number in the calculation with the least significant digits. Here, we found:
- 920.7 has 4 significant figures.
- 4.32 has 3 significant figures.
Thus, the result should be reported with 3 significant figures (the smallest number).
Step 4: Round the Result
The initial calculation gave us approximately \( 213.54 \). To round this to 3 significant figures:
- The first three significant digits in \( 213.54 \) are \( 213 \).
- The fourth digit is \( 5 \), which will round \( 213 \) up to \( 214 \).
Final Answer
Thus, the final answer with the correct number of significant digits is:
\[ \text{Answer} = 214 \]
Summary
- Calculator Answer: \( 213.54 \)
- Significant Digits Answer: \( 214 \)
- Number of Significant Digits Used: \( 3 \)