Answer the following question in scientific notation rounded to 2 decimal places. Do not show your work here. Note: We only accept scientific notation including “E”. Use 1.23E5 to represent 1.23 x 10^5. 1) (5.42E03)(4.35E-01)(6.35E-09) = E-2 2) (7.53E02)(4.92E07)(3.98E-02) = E-3 3) (6.98E-05)(1.56E07)(2.92E08) = E-4 4) (3.39E00)(3.14E01)(3.66E07) = E-5 5) (4.21E-02)(5.48E-08)(3.13E-06) = F-1 6) [(3.98E-01)(7.60E11)] ÷ (6.30E-13) = F-2 7) [(8.31E01)(3.11E13)] ÷ (5.38E-00) = F-3 8) [(8.76E-04)(9.66E17)] ÷ (2.98E11) = F-4 9) [(6.47E05)(8.00E16)] ÷ (3.58E24) = F-5 10) [(8.13E01)(8.50E-01)] ÷ (3.68E05)
The Correct Answer and Explanation is:
Here are the correct answers in scientific notation as requested:
- (5.42E03)(4.35E-01)(6.35E-09) = 1.50E-5
- (7.53E02)(4.92E07)(3.98E-02) = 1.48E8
- (6.98E-05)(1.56E07)(2.92E08) = 3.18E11
- (3.39E00)(3.14E01)(3.66E07) = 3.90E9
- (4.21E-02)(5.48E-08)(3.13E-06) = 7.23E-15
- [(3.98E-01)(7.60E11)] ÷ (6.30E-13) = 4.80E23
- [(8.31E01)(3.11E13)] ÷ (5.38E-00) = 4.81E13
- [(8.76E-04)(9.66E17)] ÷ (2.98E11) = 2.84E3
- [(6.47E05)(8.00E16)] ÷ (3.58E24) = 1.45E-2
- [(8.13E01)(8.50E-01)] ÷ (3.68E05) = 1.88E-4
Textbook-style Explanation (300 words):
In scientific notation, numbers are expressed in the form of a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. The notation aEn is used as shorthand, where “E” denotes “× 10 raised to the power”.
Multiplying numbers in scientific notation involves multiplying their coefficients and adding their exponents. For example:
(2.0E3) × (3.0E4) = (2.0 × 3.0)E(3 + 4) = 6.0E7.
When dividing, you divide the coefficients and subtract the exponents:
(6.0E7) ÷ (2.0E3) = (6.0 ÷ 2.0)E(7 − 3) = 3.0E4.
When working with mixed operations (e.g., multiplication and division), apply the order of operations (PEMDAS), ensuring to combine powers of ten appropriately.
Always round the final coefficient to two decimal places and adjust the exponent if the number exceeds or falls below the range of 1 ≤ a < 10. For instance, if your result is 12.5E5, rewrite it as 1.25E6.
Use this approach for all calculations involving scientific notation. Calculations involving very large or small numbers become simpler and easier to read when expressed this way, especially in scientific or engineering fields.
The final results above reflect correct application of multiplication and division rules in scientific notation, each rounded to two decimal places as required.
