Question

A person measures mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

• A. 661.845 g
• B. 662 g
• C. 661.8 g
• D. 661.84 g

Hint:

When adding or subtracting measurements, the result should have the same number of decimal places as the measurement with the fewest decimal places.

Answer 1

The Correct Option is C

To determine the sum of masses with appropriate significant figures, we analyze the provided measurements:

1. The given masses are 435.42 g, 226.3 g, and 0.125 g.
2. The rule for addition/subtraction with significant figures mandates rounding the result to the fewest decimal places present in any of the numbers involved.

We identify the decimal places for each measurement:

• 435.42 g has 2 decimal places.
• 226.3 g has 1 decimal place.
• 0.125 g has 3 decimal places.

The measurement with the fewest decimal places is 226.3 g, possessing 1 decimal place. Therefore, the final sum must be rounded to 1 decimal place.

1. The masses are added:

\[ 435.42 \, \text{g} + 226.3 \, \text{g} + 0.125 \, \text{g} = 661.845 \, \text{g} \]

1. Rounding 661.845 g to 1 decimal place yields 661.8 g.
2. Consequently, the sum of the masses, respecting significant figures, is 661.8 g.

The accurate result is thus 661.8 g.

This outcome is correct because it adheres to the rule of using the least number of decimal places in addition, a crucial aspect of significant figure arithmetic.