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

17.0 + 14 - 8.9

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1 answer

To evaluate the expression \(17.0 + 14 - 8.9\) and identify the significant digits, we'll go through the calculation step by step.

Step 1: Identify Significant Digits

  1. 17.0 has three significant digits (the zero after the decimal counts).
  2. 14 has two significant digits (14 is an integer).
  3. 8.9 has two significant digits (the nine after the decimal counts).

Step 2: Perform the Calculation

First, we perform the addition and subtraction:

  1. Addition: \[ 17.0 + 14 = 31.0 \]

    Here, since 17.0 (3 significant digits, decimal) and 14 (2 significant digits, no decimal) are involved, the result should be rounded to the least precise measurement's decimal place, which is the tenths place (from 17.0).

  2. Subtraction: \[ 31.0 - 8.9 = 22.1 \]

    In the subtraction step, 31.0 has a decimal place (1 decimal) whereas 8.9 has 1 decimal place as well. Therefore, we keep one decimal in our final answer.

Final Result

The final result is: \[ 22.1 \]

Step 3: Identify Significant Digits in the Final Result

The result \(22.1\) has three significant digits:

  • The digits 2 and 2 are significant.
  • The digit 1 is significant because it is a non-zero digit.

Summary

  • Calculator Answer: \(22.1\)
  • Significant Digits Answer: \(22.1\) (3 significant digits)
  • Number of Significant Digits: 3 (in \(22.1\))

Thus, the final result shown with calculations and significant digits is clear: \[ \text{Final Answer: } 22.1 \quad (\text{3 significant digits}) \]