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From the point of the view of significan...

From the point of the view of significant figures which of the following statements are correct ?
(i) `10.2 cm + 8 cm = 18. 2 cm `
(ii) ` 2.53 m - 1.2 m = 1.33 m`
(iii) `4.2 m xx 1.4 m = 5.88 m^(2)`
(iv) `3.6 m //1.75 sec = 2.1 m//s`

A

(i) & (iv) only

B

(ii) & (iii) only

C

(iv) only

D

(ii) & (iv) only

Text Solution

AI Generated Solution

The correct Answer is:
To determine which statements about significant figures are correct, we will analyze each statement step by step. ### Step 1: Analyze Statement (i) `10.2 cm + 8 cm = 18.2 cm` - **Calculation**: - 10.2 cm has 3 significant figures. - 8 cm has 1 significant figure. - **Rule**: In addition, the result should be reported to the least number of decimal places. The number with the least decimal places is 8 cm (0 decimal places). - **Result**: The answer should be rounded to 18 cm (0 decimal places). - **Conclusion**: The statement `10.2 cm + 8 cm = 18.2 cm` is **incorrect**. ### Step 2: Analyze Statement (ii) `2.53 m - 1.2 m = 1.33 m` - **Calculation**: - 2.53 m has 3 significant figures. - 1.2 m has 2 significant figures. - **Rule**: In subtraction, the result should be reported to the least number of decimal places. The number with the least decimal places is 1.2 m (1 decimal place). - **Result**: The answer should be rounded to 1.3 m (1 decimal place). - **Conclusion**: The statement `2.53 m - 1.2 m = 1.33 m` is **incorrect**. ### Step 3: Analyze Statement (iii) `4.2 m x 1.4 m = 5.88 m²` - **Calculation**: - 4.2 m has 2 significant figures. - 1.4 m has 2 significant figures. - **Rule**: In multiplication, the result should be reported to the least number of significant figures. Both numbers have 2 significant figures. - **Result**: The answer should be rounded to 5.9 m² (2 significant figures). - **Conclusion**: The statement `4.2 m x 1.4 m = 5.88 m²` is **incorrect**. ### Step 4: Analyze Statement (iv) `3.6 m / 1.75 sec = 2.1 m/s` - **Calculation**: - 3.6 m has 2 significant figures. - 1.75 sec has 3 significant figures. - **Rule**: In division, the result should be reported to the least number of significant figures. The number with the least significant figures is 3.6 m (2 significant figures). - **Result**: The answer should be rounded to 2.1 m/s (2 significant figures). - **Conclusion**: The statement `3.6 m / 1.75 sec = 2.1 m/s` is **correct**. ### Final Conclusion: Only the fourth statement is correct. Therefore, the correct answer is that only statement (iv) is valid. ---
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