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In the context of accuracy of measuremen...

In the context of accuracy of measurement and significant figures in expressing result of experiment, which of the following is /are correct
(1) Out of the two measurements 50.14 cm and `0.00025` ampere, the first one has greater accuracy
(2) If one travels 478 km by rail and 397 m by road,, the total distance travelled is 478 km

A

Only (1) is correct

B

Only (2) is correct

C

both are correct

D

none of them is correct

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The correct Answer is:
To solve the problem, we need to analyze the two statements provided regarding accuracy of measurement and significant figures. ### Step 1: Analyze the First Statement The first statement compares two measurements: 50.14 cm and 0.00025 A. We need to determine which measurement has greater accuracy based on significant figures. - **Measurement 1:** 50.14 cm has **4 significant figures** (5, 0, 1, and 4). - **Measurement 2:** 0.00025 A has **2 significant figures** (2 and 5). Since accuracy is directly proportional to the number of significant figures, **50.14 cm has greater accuracy** than 0.00025 A. Therefore, the first statement is **true**. ### Step 2: Analyze the Second Statement The second statement discusses the total distance traveled: 478 km by rail and 397 m by road. - **Distance 1:** 478 km (no decimal places). - **Distance 2:** 397 m needs to be converted to kilometers: \[ 397 \text{ m} = \frac{397}{1000} \text{ km} = 0.397 \text{ km} \] Now, we add the two distances: \[ \text{Total Distance} = 478 \text{ km} + 0.397 \text{ km} = 478.397 \text{ km} \] However, according to the rules of significant figures, the total distance must be expressed in a way that reflects the least precise measurement. The measurement 478 km has no decimal places, while 0.397 km has three decimal places. Therefore, we must round the total distance to the nearest whole number: \[ \text{Rounded Total Distance} = 478 \text{ km} \] Thus, the second statement is also **true**. ### Conclusion Both statements are correct. Therefore, the answer is that both statements are true. ### Final Answer Both statements are correct. ---

To solve the problem, we need to analyze the two statements provided regarding accuracy of measurement and significant figures. ### Step 1: Analyze the First Statement The first statement compares two measurements: 50.14 cm and 0.00025 A. We need to determine which measurement has greater accuracy based on significant figures. - **Measurement 1:** 50.14 cm has **4 significant figures** (5, 0, 1, and 4). - **Measurement 2:** 0.00025 A has **2 significant figures** (2 and 5). ...
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