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

Question

10. / 3
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Answer 1

To perform the division \( 10 \div 3 \) and identify significant digits, let's follow these steps:

Step 1: Perform the Calculation

Perform the division using a calculator:

\[ 10 \div 3 = 3.3333\overline{3} \]

Step 2: Analyze the Significant Digits

1. Identifying Significant Digits:

   • The number 10 has 2 significant digits (the digits 1 and 0).
   • The number 3 has 1 significant digit (the digit 3).

   When performing calculations, the result should be reported with the least number of significant digits based on the input values.

2. Determining the Number of Significant Digits in the Result:

   • Since 3 (the divisor) has the least significant digits (1 significant digit), the result should be rounded to 1 significant digit.

Step 3: Rounding the Result

From the calculated result \(3.3333\overline{3}\):

• To round \(3.3333\overline{3}\) to 1 significant digit, we look at the first digit (3) and the second digit (3) to determine whether to round up or down.
• Because the second digit (3) is less than 5, we round down and keep just the first digit.

Thus, \(3.3333\) rounded to 1 significant digit becomes:

\[ \text{Rounded result} = 3 \]

Conclusion

• Calculator Answer: \(3.3333\overline{3}\)
• Significant Digits Answer: \(3\)
• Number of Significant Digits: \(1\)

This process illustrates how to perform the calculation with significant digits consideration step by step.