Question

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(149.2+0.034+2000.34\) b. \(1.0322 \times 10^{3}+4.34 \times 10^{3}\) c. \(4.03 \times 10^{-2}-2.044 \times 10^{-3}\) d. \(2.094 \times 10^{5}-1.073 \times 10^{6}\)

Short answer

a. \(2149.6\) b. \(5.37 \times 10^{3}\) c. \(0.0383\) d. \(-8.646 \times 10^{5}\)

Step-by-step solution

a. Evaluate 149.2+0.034+2000.34

Step 1: Line up the decimal points and add each number \(149.2\) \(+\ \ \ 0.034\) \(+2000.34\) ____________ \( 2149.574\) Step 2: Identify the least number of decimal places in the given numbers (149.2 has 1 decimal place) Step 3: Round the sum to the same number of decimal places (1 decimal place) Final answer: \(2149.6\)

b. Evaluate \(1.0322 \times 10^{3}+4.34 \times 10^{3}\)

Step 1: Convert each number into standard form \(1.0322 \times 10^{3} = 1032.2\) \(4.34 \times 10^{3} = 4340\) Step 2: Add the numbers \(1032.2 + 4340 = 5372.2\) Step 3: Identify the least number of significant figures (4.34 has 3 significant figures) Step 4: Round the sum to the same number of significant figures (3 significant figures) Final answer: \(5.37 \times 10^{3}\)

c. Evaluate \(4.03 \times 10^{-2}-2.044 \times 10^{-3}\)

Step 1: Convert each number into standard form \(4.03 \times 10^{-2} = 0.0403\) \(2.044 \times 10^{-3} = 0.002044\) Step 2: Subtract the numbers \(0.0403 - 0.002044 = 0.038256\) Step 3: Identify the least number of decimal places in the given numbers (0.0403 has 4 decimal places) Step 4: Round the difference to the same number of decimal places (4 decimal places) Final answer: \(0.0383\)

d. Evaluate \(2.094 \times 10^{5}-1.073 \times 10^{6}\)

Step 1: Convert each number into standard form \(2.094 \times 10^{5} = 209400\) \(1.073 \times 10^{6} = 1073000\) Step 2: Subtract the numbers \(-1073000 + 209400 = -864600\) Step 3: Identify the least number of significant figures (1.073 has 4 significant figures) Step 4: Round the difference to the same number of significant figures (4 significant figures) Final answer: \(-8.646 \times 10^{5}\)