Question

From the point of view of significant figures, which of the following is/are correct? (i) $1.3~cm + 4~cm = 15.3~cm$ (ii) $4.53~m - 1.2~m = 3.3~m$ (iii) $5.45~kg - 3.2~kg = 2.25~kg$ (iv) $4.8~cm + 48.6~cm = 133~cm$

• A. (ii) only
• B. (iv) only
• C. (i) & (iii)
• D. (ii) & (iv)

Hint:

Addition/Subtraction rule: Least precise decimal place wins!

Answer 1

The Correct Option is A

Step 1: The rule we use.
This is about significant figures in adding and subtracting. The key idea is simple: when you add or subtract numbers, the answer can keep only as many decimal places as the number that has the fewest decimal places. So we round the final result to the least precise decimal position.

Step 2: Why this rule makes sense.
A measurement is only as trustworthy as its least precise part. If one value is known only to one decimal place, the sum cannot pretend to know more than that. So we let the weakest measurement decide the precision of the answer.

Step 3: Check option (i).
Here $1.3 + 4 = 5.3$, not $15.3$. The stated result is simply wrong, so (i) is incorrect.

Step 4: Check option (ii).
Here $4.53 - 1.2 = 3.33$. The number $1.2$ has only one decimal place, so we round to one decimal place: $3.33 \to 3.3$. The stated value is $3.3$, which matches. So (ii) is correct.

Step 5: Check option (iii).
Here $5.45 - 3.2 = 2.25$. Rounding to one decimal place (because $3.2$ has one) gives $2.3$, not $2.25$. So (iii) is incorrect.

Step 6: Check option (iv).
Here $4.8 + 48.6 = 53.4$, not $133$. So (iv) is incorrect.

Step 7: Conclusion.
Only statement (ii) follows the significant figure rules correctly. \[ \boxed{\text{(ii) only}} \]