Final answer:
To multiply numbers in scientific notation, multiply the coefficients and add the exponents. The given expression equals 4.516518 × 10⁶. The coefficent is adjusted to respect significant figures for proper scientific notation.
Step-by-step explanation:
Multiplying numbers in scientific notation involves multiplying the base numbers and adding the exponents. For the given expression (4.506 × 104 × 1.003 × 102), we first multiply the coefficients 4.506 and 1.003. This yields approximately 4.516518 after multiplication. Next, we add the exponents of 10 since we are dealing with scientific notation, meaning 4 + 2 to get an exponent of 6. Thus, the expression simplifies to (4.516518 × 106). However, if we are to express this in proper scientific notation, the coefficient must be between 1 and 10, so we adjust the coefficient to 4.516518 by moving the decimal point one place to the left, which increases the exponent by 1, resulting in a final answer of (4.516518 × 106) or more precisely 4.516518 × 106 to respect the significant figures.