Questions: Using the rules of significant figures, calculate the following: (6.485+7.041)/3.73+0.278

Using the rules of significant figures, calculate the following: (6.485+7.041)/3.73+0.278
Transcript text: Using the rules of significant figures, calculate the following: \[ \frac{6.485+7.041}{3.73}+0.278 \]
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Solution

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Solution Steps

To solve this problem, first perform the addition in the numerator. Then, divide the result by the denominator. Finally, add the given number to the result of the division. Throughout the calculation, apply the rules of significant figures: the result of addition or subtraction should have the same number of decimal places as the number with the fewest decimal places, and the result of multiplication or division should have the same number of significant figures as the number with the fewest significant figures.

Step 1: Calculate the Numerator

First, we perform the addition in the numerator: \[ 6.485 + 7.041 = 13.526 \] The result, \(13.526\), has three decimal places.

Step 2: Perform the Division

Next, we divide the result of the addition by the denominator: \[ \frac{13.526}{3.73} = 3.626 \] The division result, \(3.626\), is rounded to four significant figures, as the denominator \(3.73\) has three significant figures.

Step 3: Add the Additional Number

Finally, we add the additional number to the result of the division: \[ 3.626 + 0.278 = 3.904 \] The result, \(3.904\), is rounded to three decimal places, as the number \(0.278\) has three decimal places.

Final Answer

The final result of the calculation is: \[ \boxed{3.904} \]

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