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 solve the problem of determining the sum of the masses with consideration to significant figures, we start by examining the given measurements:

1. The given masses are: 435.42 g, 226.3 g, and 0.125 g.
2. The rule for addition and subtraction in significant figures states that the result should be rounded off to the least number of decimal places of any number in the operation.

Let's identify the number of decimal places in each of these measurements:

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

The measure with the least number of decimal places is 226.3 g, which has 1 decimal place. Hence, the final result of the addition needs to be rounded to 1 decimal place.

1. Add the masses together:

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

1. Round 661.845 g to 1 decimal place, which results in 661.8 g.
2. Thus, the sum of the masses, considering significant figures, is 661.8 g.

The correct answer is therefore 661.8 g.

This option is correct due to applying the rule of least decimal places in addition, which is pivotal in handling significant figures in arithmetic operations.

Answer 2

\( m_1 + m_2 + m_3 = 435.42 + 226.3 + 0.125 \) \( = 661.845 \) g According to least significant digits m = 661.8 g