Of the following which is the most precisely reported value of a speed measurement?
125.00 km/s
Understanding Measurement Precision
When reporting a measurement in science, the way the value is written tells us about its precision. Precision refers to the level of detail or the fineness of the measurement. A more precise measurement has more significant figures or is reported to a smaller fractional part.
Significant Figures and Precision
Significant figures are the digits in a number that carry meaningful contributions to its measurement resolution. They include all non-zero digits, zeros between non-zero digits, and trailing zeros in a number containing a decimal point.
Generally, a value reported with more significant figures is considered more precise, assuming the measurement was performed with a suitable instrument.
Analyzing the Speed Measurements
Let's look at each given speed measurement option and determine the number of significant figures it contains:
- Option 1: 125 km/s
- The non-zero digits (1, 2, 5) are significant.
- Number of significant figures = 3.
- Option 2: 12.5 × 10 km/s
- This value is equal to 125 km/s.
- Similar to option 1, the non-zero digits (1, 2, 5) are significant.
- Number of significant figures = 3.
- Option 3: 125.00 km/s
- The non-zero digits (1, 2, 5) are significant.
- The zeros after the decimal point and after a non-zero digit are significant. The two zeros (0, 0) are significant.
- Number of significant figures = 5.
- Option 4: 1.250 × 102 km/s
- This value is in scientific notation. The significant figures are determined from the mantissa (the part before the × 10power).
- The mantissa is 1.250. The non-zero digits (1, 2, 5) are significant. The trailing zero after the decimal point (0) is also significant.
- Number of significant figures = 4.
Comparing Precision
We can compare the precision of the measurements by looking at the number of significant figures:
| Speed Measurement | Value | Significant Figures |
|---|---|---|
| Option 1 | 125 km/s | 3 |
| Option 2 | 12.5 × 10 km/s | 3 |
| Option 3 | 125.00 km/s | 5 |
| Option 4 | 1.250 × 102 km/s | 4 |
The value with the highest number of significant figures represents the most precise measurement among the given options. Option 3, 125.00 km/s, has 5 significant figures, which is more than the other options.
Therefore, 125.00 km/s is the most precisely reported value.
Important Questions from Data Interpretation
The table shows the monthly expenditure of Saumya. What percent of her monthly salary is she able to save?
Expense Amount Food 5,000 Rent 20,000 Travel 10,000 Clothing 3,000 Miscellaneous 15,000 Savings 7,500 What does the height of the rectangle in a histogram show?
Following table provides figures (in rupees) on annual expenditure of a firm for two years – 2010 and 2011.
Category
2010
2011
Raw material
5200
6240
Power & fuel
7000
9450
Salary & wages
9000
12600
Plant & machinery
20000
25000
Advertising
15000
19500
Research & Development
22000
26400
In 2011, which of the following two categories have registered increase by same percentage?
Read the following table giving sales data of five types of batteries for years 2006 to 2012
Year
Type I
Type II
Type III
Type IV
Type V
2006
75
144
114
102
108
2007
90
126
102
84
126
2008
96
114
75
105
135
2009
105
90
150
90
75
2010
90
75
135
75
90
2011
105
60
165
45
120
2012
115
85
160
100
145
Out of the following which type of battery achieved highest growth between the years 2006 and 2012?Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A × B × C), (B × G × E) and (D × E × F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F and G?
A
D
B
G
E
C
F
