Question

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:

• A. \( y = 1326.2 \)
• B. \( y = 1326.19 \)
• C. \( y = 1326.186 \)
• D. \( y = 1330 \)

Hint:

When performing calculations involving significant figures, always round the result to the least number of significant figures in the given data.

Answer 1

The Correct Option is D

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:

1. 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.
2. 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: \(36300\).
3. 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.
4. 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.

Answer 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 \( \boxed{1330} \).