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show the calculator answer, significant digits answer and identify the number of significant digits. show all work.

35.7 x 0.78 x 2.3

make it more clear.

1 answer

To solve the expression \( 35.7 \times 0.78 \times 2.3 \) while paying attention to significant figures, we will follow these steps:

Step 1: Perform the Calculation

First, let's do the multiplication:

  1. Calculate \( 35.7 \times 0.78 \): \[ 35.7 \times 0.78 = 27.846 \]

  2. Now multiply the result by \( 2.3 \): \[ 27.846 \times 2.3 = 64.0368 \]

Step 2: Determine Significant Figures

Now we need to determine how many significant figures each of our original numbers have:

  • 35.7 has 3 significant figures.
  • 0.78 has 2 significant figures.
  • 2.3 has 2 significant figures.

Step 3: Identify the Limiting Significant Figures

The result of a multiplication should be reported with the same number of significant figures as the measurement that has the least number of significant figures. In this case, both \( 0.78 \) and \( 2.3 \) have 2 significant figures, which is the least.

Step 4: Round the Final Answer

The calculated result is \( 64.0368 \). Since we need to round this to 2 significant figures, we take only the first two digits (6 and 4) and look at the next digit (0) to decide whether to round up or stay the same.

Since 0 is less than 5, we leave it as is:

Thus, rounding \( 64.0368 \) to 2 significant figures gives us 64.

Final Answers

  • Calculator Answer: \( 64.0368 \)
  • Final Answer (with significant digits): \( 64 \)
  • Number of Significant Digits: 2 significant digits

This concludes the calculation with all steps clearly laid out!