Question

perform the calculation to the correct number of significant figures.
3.10007 × 9.441 × 0.0301 ÷ 2.31
express your answer using the appropriate significant figures.
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Explanation:

Step1: Multiply the first two numbers

First, multiply \( 3.10007 \) and \( 9.441 \).
\( 3.10007\times9.441 = 29.26776087 \)

Step2: Multiply the result by 0.0301

Next, multiply the above result by \( 0.0301 \).
\( 29.26776087\times0.0301 = 0.8809596022 \)

Step3: Divide by 2.31

Now, divide the result by \( 2.31 \).
\( 0.8809596022\div2.31 \approx 0.381367 \)

Step4: Determine significant figures

The least number of significant figures in the given numbers is 3 (from \( 0.0301 \) and \( 2.31 \)). So we round the result to 3 significant figures.
\( 0.381367 \approx 0.381 \) (Wait, no, wait. Wait, let's check the significant figures again. Wait, \( 3.10007 \) has 6 sig figs, \( 9.441 \) has 4, \( 0.0301 \) has 3, \( 2.31 \) has 3. When multiplying and dividing, the result should have the same number of sig figs as the least precise measurement, which is 3. Wait, but let's recalculate the multiplication and division more accurately.

Wait, let's do the calculation step by step with more precision:

First, \( 3.10007 \times 9.441 = 3.10007\times9 + 3.10007\times0.441 = 27.90063 + 1.36713087 = 29.26776087 \)

Then, \( 29.26776087\times0.0301 = 29.26776087\times0.03 + 29.26776087\times0.0001 = 0.8780328261 + 0.002926776087 = 0.8809595922 \)

Then, \( 0.8809595922\div2.31 \). Let's do this division:

\( 0.8809595922\div2.31 \approx 0.381367 \)

Now, the number with the least significant figures is \( 0.0301 \) (3 sig figs) and \( 2.31 \) (3 sig figs). So we round to 3 sig figs. Wait, but \( 0.381367 \) rounded to 3 sig figs is \( 0.381 \)? Wait, no, wait: the first non-zero digit is 3, then 8, then 1, then 3. So 3.81 x 10^-1, which is 0.381. Wait, but let's check again. Wait, maybe I made a mistake in the significant figures. Wait, \( 3.10007 \) has 6, \( 9.441 \) has 4, \( 0.0301 \) has 3, \( 2.31 \) has 3. So the result should have 3 significant figures. So \( 0.381 \) is correct? Wait, but let's check the calculation again. Wait, maybe I miscalculated the multiplication and division. Let's use a calculator:

3.10007 * 9.441 = 29.26776087

29.26776087 * 0.0301 = 0.8809596022

0.8809596022 / 2.31 = 0.38136736

Now, rounding to 3 significant figures: the first three significant figures are 3, 8, 1. The next digit is 3, which is less than 5, so we keep it 0.381. Wait, but maybe the correct answer is 0.381? Wait, but let's check again. Wait, maybe I made a mistake in the significant figures. Wait, \( 0.0301 \) has three significant figures (3, 0, 1? No, wait: leading zeros are not significant, so 0.0301 has three significant figures: 3, 0, 1? Wait, no: 0.0301 is 3.01 x 10^-2, so three significant figures. \( 2.31 \) is three significant figures. So the result should have three significant figures. So 0.381 is correct. Wait, but maybe the answer is 0.381? Wait, but let's check with another approach. Let's do the calculation as (3.10007 9.441 0.0301) / 2.31. Let's compute numerator first: 3.10007 9.441 = 29.26776087; 29.26776087 0.0301 = 0.8809596022; then divide by 2.31: 0.8809596022 / 2.31 ≈ 0.381. So the answer is 0.381.

Answer:

\( 0.381 \)