Question

Do the calculations, round off your answers to the correct number of significant figures and express the answer in proper exponential notation.

A. 2.23 X 10⁷ * 3.0 X 10⁻4
B. 2.21 X 10⁷/5.500 X 10⁻4
C. 2.2 X 10 ⁻2 + 3.13 X 10³
D. 7.63 X 10⁻2 - 3.15 X 10⁻4

Answer 1

To multiply or divide numbers in scientific notation, multiply or divide the coefficients and add or subtract the exponents. Round the final answer to the correct number of significant figures and express it in proper exponential notation.

Step-by-step explanation:

In order to multiply or divide numbers written in scientific notation, you simply multiply or divide the coefficients and add or subtract the exponents. Let's go through each calculation:

A. (2.23 x 10⁷) x (3.0 x 10⁻⁴) = (2.23 x 3.0) x (10⁷ x 10⁻⁴) = 6.69 x 10³

B. (2.21 x 10⁷) / (5.500 x 10⁻⁴) = (2.21 / 5.500) x (10⁷ / 10⁻⁴) = 0.4017 x 10¹¹ = 4.017 x 10¹⁰

C. (2.2 x 10⁻²) + (3.13 x 10³) = (0.022) + (3130) = 3130.022 = 3.13 x 10³ (rounded to 2 significant figures)

D. (7.63 x 10⁻²) - (3.15 x 10⁻⁴) = (0.0763) - (0.000315) = 0.076 - 0.0003 = 0.0757 (rounded to 3 significant figures)