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 given below shows the earnings of two persons on five different days.
What is the ratio of total earnings of P to the total earnings of Q?Earnings Days P Q Monday 105 150 Tuesday 96 110 Wednesday 65 122 Thursday 115 106 Friday 130 68 The table below shows the number of toys of 6 different colours sold from a shop during a given period. The table also shows the percentage of toys of each colour which are cars.
Colour Total toys Percentage of cars C1 500 12 C2 600 15 C3 400 12.5 C4 550 10 C5 650 20 C6 450 10 What is the total number of car toys of C2 and C3 taken together?
Study the given graph carefully and answer the question that follows. The graph shows the demand and production of different companies.
The ratio between the companies having more production than demand and more demand than production is:
Study the given table and answer the question that follows. The given table shows the number of new employees added to different categories of employees in a company for four years and the number of employees from these categories who left the company every year.
During the period between 2001 and 2004, the total number of Technicians who left the Company is what percentage (rounded off to the nearest integer) of the total number of Technicians who joined the Company?
The given pie-chart shows the percentage distribution of 20,000 employees in a company. Study the given chart and answer the question that follows. If 30% of the employees in department D are females, then how many male employees are there in that department?
