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Answer :
To solve the problems involving significant figures in calculations, we follow specific rules for addition and subtraction. Here's how it works for each calculation:
1. Addition: [tex]\(31.580 + 4.26\)[/tex]
- Identify the decimal places: In addition, we align numbers by their decimal points and pay attention to the number of decimal places.
- [tex]\(31.580\)[/tex] has 3 decimal places.
- [tex]\(4.26\)[/tex] has 2 decimal places.
- Rule for addition/subtraction: The result should have the same number of decimal places as the number with the fewest decimal places from the original numbers.
- Perform the calculation:
[tex]\[
31.580 + 4.26 = 35.840
\][/tex]
- Round to 2 decimal places (the fewest in original numbers).
- Final result: 35.84
2. Subtraction: [tex]\(1.0250 - 0.00063\)[/tex]
- Identify the decimal places: Both numbers have different numbers of decimal places.
- [tex]\(1.0250\)[/tex] has 4 decimal places.
- [tex]\(0.00063\)[/tex] has 5 decimal places.
- Rule for addition/subtraction: The result should have the same number of decimal places as the number with the fewest decimal places from the original numbers.
- Perform the calculation:
[tex]\[
1.0250 - 0.00063 = 1.02437
\][/tex]
- Round to 5 decimal places (the fewest in original numbers, which is more precise).
- Final result: 1.02437
The results of the calculations are 35.84 and 1.02437.
1. Addition: [tex]\(31.580 + 4.26\)[/tex]
- Identify the decimal places: In addition, we align numbers by their decimal points and pay attention to the number of decimal places.
- [tex]\(31.580\)[/tex] has 3 decimal places.
- [tex]\(4.26\)[/tex] has 2 decimal places.
- Rule for addition/subtraction: The result should have the same number of decimal places as the number with the fewest decimal places from the original numbers.
- Perform the calculation:
[tex]\[
31.580 + 4.26 = 35.840
\][/tex]
- Round to 2 decimal places (the fewest in original numbers).
- Final result: 35.84
2. Subtraction: [tex]\(1.0250 - 0.00063\)[/tex]
- Identify the decimal places: Both numbers have different numbers of decimal places.
- [tex]\(1.0250\)[/tex] has 4 decimal places.
- [tex]\(0.00063\)[/tex] has 5 decimal places.
- Rule for addition/subtraction: The result should have the same number of decimal places as the number with the fewest decimal places from the original numbers.
- Perform the calculation:
[tex]\[
1.0250 - 0.00063 = 1.02437
\][/tex]
- Round to 5 decimal places (the fewest in original numbers, which is more precise).
- Final result: 1.02437
The results of the calculations are 35.84 and 1.02437.
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