Question

Add \( 2.7 \times 10^{-5} \) to \( 4.5 \times 10^{-4} \) with due regard to significant figures

• A. \( 4.8 \times 10^{-4} \)
• B. \( 4.7 \times 10^{-5} \)
• C. \( 4.8 \times 10^{-5} \)
• D. \( 4.7 \times 10^{-4} \)
• E. \( 5.0 \times 10^{-4} \)

Hint:

In addition and subtraction of numbers in scientific notation, align the exponents and round according to the least number of decimal places in the original values.

Answer 1

The Correct Option is A

We are given \( 2.7 \times 10^{-5} \) and \( 4.5 \times 10^{-4} \), and we are required to add them with due regard to significant figures. 
Step 1: Convert the numbers into the same order of magnitude. We can rewrite \( 2.7 \times 10^{-5} \) as: \[ 2.7 \times 10^{-5} = 0.27 \times 10^{-4}. \] 
Step 2: Now, we can add the numbers: \[ 0.27 \times 10^{-4} + 4.5 \times 10^{-4} = 4.77 \times 10^{-4}. \] 
Step 3: Next, we need to round the result according to significant figures. The number \( 4.5 \times 10^{-4} \) has 2 significant figures, so the result should also have 2 significant figures: \[ 4.77 \times 10^{-4} \approx 4.8 \times 10^{-4}. \] 
Thus, the final answer is \( \boxed{4.8 \times 10^{-4}} \).