For an experimental expression \( y = \frac{32.3 \times 1125}{27.4} \), where all the digits are significant. Then to report the value of \( y \), we should write:
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- \( y = 1326.2 \)
- \( y = 1326.19 \)
- \( y = 1326.186 \)
- \( y = 1330 \)
The Correct Option is D
Approach Solution - 1
To solve the problem, we need to evaluate the expression and determine the correct number of significant figures in the result. The given expression is:
\(y = \frac{32.3 \times 1125}{27.4}\)
To determine the final number of significant figures, follow these steps:
- Identify the number of significant figures in each term:
- \(32.3\) has 3 significant figures.
- \(1125\) has 4 significant figures.
- \(27.4\) has 3 significant figures.
- Multiply \(32.3\) by \(1125\). The product will have the smallest number of significant figures present in the multiplied numbers, which is 3.
- Calculation: \(32.3 \times 1125 = 36337.5\) (but retain 3 significant figures only).
- Rounded to 3 significant figures: \(36300\).
- Divide the result by \(27.4\):
- Calculation: \(\frac{36300}{27.4} = 1325.9124\ldots\)
- Since the division involves 3 significant figures from both the numerator and the denominator, we round the result to 3 significant figures.
- Round \(1325.9124\ldots\) to 3 significant figures: \(1330\).
Therefore, the value of \(y\) should be reported as:
- \(y = 1330\).
This solution uses correct significant figure rules and arithmetic to arrive at the answer \(y = 1330\), matching the given correct option.
Approach Solution -2
Given the experimental expression:
\[ y = \frac{32.3 \times 1125}{27.4}, \] where all the digits are significant.
Step 1: Determine the significant figures
The number of significant figures in each of the values is: - \( 32.3 \) has 3 significant figures. - \( 1125 \) has 4 significant figures. - \( 27.4 \) has 3 significant figures. According to the rules of significant figures: - When multiplying or dividing, the result should have the same number of significant figures as the value with the fewest significant figures. Therefore, the result should have 3 significant figures.
Step 2: Perform the calculation
First, calculate the expression: \[ y = \frac{32.3 \times 1125}{27.4} \approx \frac{36337.5}{27.4} \approx 1330.05. \]
Step 3: Round the result
Rounding to 3 significant figures gives: \[ y \approx 1330. \]
Final Answer:
The value of \( y \) should be reported as \( \boxed{1330} \).
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