Perform the calculation to the correct number of significant figures.
2.5110 x 21.20÷(44.11+1.223)
The Correct Answer and Explanation is :
The correct answer, rounded to four significant figures, is 1.174.
Explanation:
- Understanding Significant Figures:
- Significant figures in a number indicate the precision of a measurement. When performing calculations, the result should reflect the least precise measurement used.
- Given Values and Their Significant Figures:
- (2.5110) has 5 significant figures.
- (21.20) has 4 significant figures.
- (44.11 + 1.223 = 45.333), where (44.11) has 4 significant figures and (1.223) has 4 significant figures. The sum, (45.333), retains 4 significant figures.
- Step-by-Step Calculation:
- First, multiply (2.5110 \times 21.20 = 53.2332).
- Then, divide by (45.333):
[
\frac{53.2332}{45.333} = 1.1743
]
- Applying Significant Figure Rules:
- In multiplication and division, the result should have the same number of significant figures as the least precise measurement.
- The least number of significant figures among the numbers used is 4 (from (21.20) and (45.333)).
- Therefore, the final result is rounded to 1.174 (4 significant figures).
Now, I will generate a visual representation of this calculation.
The bar chart visually represents each step of the calculation, showing how we progress from multiplication to division and finally rounding to the correct number of significant figures. Let me know if you need further clarification!
