The number of significant figures in $\frac{25 \times 0.524}{100.0} = 0.131$ is
Significant Figures in Calculations
This question asks us to determine the number of significant figures for the result of a calculation involving multiplication and division. We need to apply the standard rules for significant figures.
Input Numbers and Significant Figures
First, let's examine the numbers involved in the calculation $\frac{25 \times 0.524}{100.0}$ and identify the number of significant figures in each:
| Number | Significant Figures | Reasoning |
| $25$ | 2 | This number has two non-zero digits, both of which are significant. |
| $0.524$ | 3 | The zero before the decimal point is not significant. The digits 5, 2, and 4 are significant. |
| $100.0$ | 4 | Zeros are significant if they are after the decimal point and are trailing zeros. Here, the trailing zero after '$100.$' is significant. |
Multiplication and Division Rules
The rules for significant figures in multiplication and division state that the final answer should be rounded to have the same number of significant figures as the measurement having the fewest significant figures.
- In our calculation, the numbers have 2 significant figures ($25$), 3 significant figures ($0.524$), and 4 significant figures ($100.0$).
- The minimum number of significant figures among these input values is 2, which comes from the number $25$.
Resulting Significant Figures
Based on the rule, the result of the calculation $\frac{25 \times 0.524}{100.0}$ must be reported with only 2 significant figures to maintain the appropriate level of precision.
The actual numerical result of the calculation is $0.131$. However, applying the significant figures rule means we must round this result. Since the least precise input had 2 significant figures, our result should also have 2 significant figures. Rounding $0.131$ to two significant figures gives $0.13$.
Therefore, the number of significant figures in the final, correctly reported result of this calculation is 2.
Conclusion on Significant Figures
The number of significant figures determined by the rules for the calculation $\frac{25 \times 0.524}{100.0}$ is 2.
Important Questions from Numerical Estimation
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The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is
Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation.
Given the data below, which room will Ajit stay in?
Names
Student seniority
Current
Room preference list
Amar
1
P
R, S, Q
Akbar
2
None
R, S
Anthony
3
Q
P
Ajit
4
S
Q, P, R
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