Question

Two physical quantities \( x \) and \( y \) have measured values 23.01 and 37.3 respectively. Then the value of \( x + y \) is:

• A. 60.3
• B. 60.31
• C. 60.03
• D. 60.310

Hint:

When adding or subtracting measured quantities, the result should have the same number of decimal places as the least precise value.

Answer 1

The Correct Option is A

Step 1: Analyze the significant figures.
The given values of \( x = 23.01 \) and \( y = 37.3 \) are measured with different numbers of significant figures. - \( x = 23.01 \) has 4 significant figures. - \( y = 37.3 \) has 3 significant figures. When performing addition or subtraction, the result should be reported with the same number of decimal places as the value with the least number of decimal places.
Step 2: Add the values.
Performing the addition: \[ x + y = 23.01 + 37.3 = 60.31 \] However, since \( y = 37.3 \) has only one decimal place, the result should be rounded to one decimal place.
Step 3: Round the result.
The sum \( 60.31 \) is rounded to \( 60.3 \) because it has to match the least number of decimal places (1 decimal place) from the given values. Thus, the value of \( x + y \) is \( 60.3 \).