Question

With due regard to significant figures, add the following
a. $953$ and $0.324$
b. $953$ and $0.625$
c. $953.0$ and $0.324$
d. $953.0$ and $0.374$

(A) a. $953$; b. $954$; c. $953.3$; d. $953.4$
(B) a. $953$; b. $955$; c. $953.3$; d. $953.4$
(C) a. $952$; b. $954$; c. $953.3$; d. $953.4$
(D) a. $953$; b. $954$; c. $953.3$; d. $952.4$

Answer 1

Hint
After doing the addition we have to round off the figures, The final answer will be the number of digits to the right of decimal place as in the number with the least number of digits to the right of decimal place.

Complete step by step answer
To find the answers with the correct number of first we perform the addition. So in the first part, the numbers are given $953$ and $0.324$. On adding these two numbers, we get,
$953 + 0.324 = 953.324$
So we can now round off the number till before the decimal place. This is because, since the number $953$ has no digit to the right of decimal place so the significant digits in the sum will have no digit to the right of the decimal point. Since the digit after the decimal place is 3, rounding off the sum will give us $953$. So the answer for part a. is $953$.
So in the second part, the numbers are given $953$ and $0.625$. On adding these two numbers, we get,
$953 + 0.625 = 953.625$
Since the number $953$ again has no digit to the right of the decimal place so the significant digits in the sum will have no digit to the right of the decimal point. Since the digit after the decimal place is 6 which is greater than 5, so on rounding off the sum will be $954$. So the answer for part b. is $954$.
So in the third part, the numbers are given $953.0$ and $0.324$. On adding these two numbers, we get,
$953.0 + 0.324 = 953.324$
Since the number $953.0$ has 1 digit to the right of the decimal place so the significant digits in the sum will have 1 digit to the right of the decimal point. So we round the number off to 1 digit after the decimal. The second digit after the decimal is 2, so rounding off will keep the first digit unchanged. Hence the answer for part c. is, $953.3$.
In the fourth part, the numbers are given $953.0$ and $0.374$. On adding these two numbers, we get,
$953.0 + 0.374 = 953.374$
Since the number $953.0$ has 1 digit to the right of the decimal place so the significant digits in the sum will have 1 digit to the right of the decimal point. So we round the number off to 1 digit after the decimal. The second digit after the decimal is 7, so rounding off will increase the first digit by 1. Therefore, the answer in the fourth part d. is $953.4$
Therefore the answers are, a. $953$; b. $954$; c. $953.3$; d. $953.4$
So the correct answer is option (A).

Note
The significant digits in any number are those that carry meaning and contribution to the measurement resolution. In a number, the most significant digit is the one that has the highest exponent value and the least significant is the one with least exponent value.