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

7.895 + 3.4

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1 answer

To solve the addition \(7.895 + 3.4\) and determine the result with the correct number of significant digits, follow these steps:

Step 1: Perform the Calculation

We'll add the two numbers together:

\[ 7.895 + 3.4 = 11.295 \]

Step 2: Determine the Significant Digits

  1. Identify Decimal Places:

    • 7.895 has three decimal places.
    • 3.4 has one decimal place.

  2. Apply the Rule for Significant Figures in Addition: The result should be rounded to the least number of decimal places of any number in the sum. In this case, we should round to one decimal place because \(3.4\) has the fewest decimal places (one).

Step 3: Round the Result

The unrounded result was \(11.295\). To round it to one decimal place:

  • Look at the second decimal place (which is \(9\)); since it's \(5\) or greater, round up the first decimal place.

Thus, \(11.295\) rounded to one decimal place becomes:

\[ 11.3 \]

Final Results Summary

  • Calculator Result: \(11.295\)
  • Significant Figures Answer: \(11.3\)
  • Number of Significant Digits in Final Answer: 3 (the digits 1, 1, and 3)

Conclusion

The final answer to \(7.895 + 3.4\) is \(11.3\) when expressed with the correct number of significant digits.