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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 of the given statements about significant figures is correct, we will analyze each statement based on the rules of significant figures in arithmetic operations. ### Step-by-Step Solution: 1. **Statement (i): `10.2 cm + 8 cm = 18.2 cm`** - **Analysis**: - `10.2 cm` has 3 significant figures (the digits 1, 0, and 2). - `8 cm` has 1 significant figure (the digit 8). - When adding, the result should be rounded to the least number of decimal places in the numbers being added. Here, `8 cm` has no decimal places, so the result should be rounded to the nearest whole number. - **Conclusion**: The correct result should be `18 cm` (not `18.2 cm`), making this statement **incorrect**. 2. **Statement (ii): `2.53 m - 1.2 m = 1.33 m`** - **Analysis**: - `2.53 m` has 3 significant figures. - `1.2 m` has 2 significant figures. - When subtracting, the result should be rounded to the least number of decimal places. `1.2 m` has 1 decimal place, so the result should be rounded to 1 decimal place. - **Conclusion**: The correct result should be `1.3 m` (not `1.33 m`), making this statement **incorrect**. 3. **Statement (iii): `4.2 m x 1.4 m = 5.88 m²`** - **Analysis**: - `4.2 m` has 2 significant figures. - `1.4 m` has 2 significant figures. - When multiplying, the result should be rounded to the least number of significant figures in the numbers being multiplied. Both numbers have 2 significant figures. - **Conclusion**: The correct result should be `5.9 m²` (not `5.88 m²`), making this statement **incorrect**. 4. **Statement (iv): `3.6 m / 1.75 sec = 2.1 m/s`** - **Analysis**: - `3.6 m` has 2 significant figures. - `1.75 sec` has 3 significant figures. - When dividing, the result should be rounded to the least number of significant figures. The result should have 2 significant figures (the least of the two). - **Conclusion**: The correct result should be `2.1 m/s`, making this statement **correct**. ### Final Summary: - Statement (i) is incorrect. - Statement (ii) is incorrect. - Statement (iii) is incorrect. - Statement (iv) is correct.
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