Problem 100 - College Algebra Essentials

Question

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $$\frac{7.5 \times 10^{-2}}{2.5 \times 10^{6}}$$

Step-by-Step Solution

Answer

Therefore, the correct answer after performing the indicated computation in scientific notation rounded to two decimal points is \( 3.00 \times 10^{-8} \).

Step 1: Divide Significant Figures

Divide the significant numbers 7.5 and 2.5 first, these are the two numeric values in the given problem. The result is \( \frac{7.5}{2.5} = 3 \).

Step 2: Subtract Exponents

Subtract the exponent of the denominator from the exponent of the numerator. In this case, subtract 6 (exponent of denominator) from -2 (exponent of numerator). The result is \( 10^{{-2-6}} = 10^{-8} \)

Step 3: Multiplication

The final answer will be the value from step 1 times the value from step 2. This gives \( 3 \times 10^{-8} \). In scientific notation, a number is expressed in the form \( a \times 10^n \) where n is an integer, and 1 ≤ a < 10. In our case, 'a' is '3', and 'n' is '-8'. So the number '3' forms the decimal portion (rounded to the two decimal places as required), and the integer '-8' represents the exponent portion.