Answer :
Sure, let's go through each calculation and determine the correct number of significant figures for each result.
a. [tex]\(100 \times 23\)[/tex]:
- Both 100 and 23 have 3 significant figures.
- In multiplication, the result should have the same number of significant figures as the factor with the least amount, which is 3 significant figures in this case.
- The calculation is: [tex]\(100 \times 23 = 2300\)[/tex].
- So, the answer with the correct significant figures is 2300.
b. [tex]\(97.5 - 43.02\)[/tex]:
- 97.5 has 3 significant figures, and 43.02 has 4 significant figures.
- For subtraction, the result should have the same number of decimal places as the number with the fewest decimal places, which here is 1 decimal place (in 97.5).
- The calculation is: [tex]\(97.5 - 43.02 = 54.48\)[/tex].
- So, the answer rounded to the correct decimal places is 54.48 (rounded to 2 decimal places from the operation).
c. [tex]\(8064 / 0.0360\)[/tex]:
- 8064 has 4 significant figures, and 0.0360 has 3 significant figures.
- In division, the result should have the same number of significant figures as the factor with the least amount, which here is 3 significant figures.
- The calculation is: [tex]\(8064 \div 0.0360 = 224000\)[/tex].
- So, the answer with the correct significant figures is 224000.
d. [tex]\(54.00 + 78\)[/tex]:
- 54.00 has 4 significant figures, and 78 has 2 significant figures.
- For addition, we consider decimal places; however, since 78 has no decimal places, the calculated answer will accommodate the least decimal places.
- The calculation is: [tex]\(54.00 + 78 = 132.00\)[/tex].
- So, the answer with the correct significant figures is 132 (considering decimal accuracy in addition).
These represent the results of each calculation rounded to the appropriate significant figures based on the rules of significant figures in mathematical operations.
a. [tex]\(100 \times 23\)[/tex]:
- Both 100 and 23 have 3 significant figures.
- In multiplication, the result should have the same number of significant figures as the factor with the least amount, which is 3 significant figures in this case.
- The calculation is: [tex]\(100 \times 23 = 2300\)[/tex].
- So, the answer with the correct significant figures is 2300.
b. [tex]\(97.5 - 43.02\)[/tex]:
- 97.5 has 3 significant figures, and 43.02 has 4 significant figures.
- For subtraction, the result should have the same number of decimal places as the number with the fewest decimal places, which here is 1 decimal place (in 97.5).
- The calculation is: [tex]\(97.5 - 43.02 = 54.48\)[/tex].
- So, the answer rounded to the correct decimal places is 54.48 (rounded to 2 decimal places from the operation).
c. [tex]\(8064 / 0.0360\)[/tex]:
- 8064 has 4 significant figures, and 0.0360 has 3 significant figures.
- In division, the result should have the same number of significant figures as the factor with the least amount, which here is 3 significant figures.
- The calculation is: [tex]\(8064 \div 0.0360 = 224000\)[/tex].
- So, the answer with the correct significant figures is 224000.
d. [tex]\(54.00 + 78\)[/tex]:
- 54.00 has 4 significant figures, and 78 has 2 significant figures.
- For addition, we consider decimal places; however, since 78 has no decimal places, the calculated answer will accommodate the least decimal places.
- The calculation is: [tex]\(54.00 + 78 = 132.00\)[/tex].
- So, the answer with the correct significant figures is 132 (considering decimal accuracy in addition).
These represent the results of each calculation rounded to the appropriate significant figures based on the rules of significant figures in mathematical operations.
