What is the product of [tex]$\left(6.5 \times 10^5\right)\left(1.02 \times 10^6\right)$[/tex] written in scientific notation?
A. [tex]$6.63 \times 10^{12}$[/tex]
B. [tex]$6.63 \times 10^{11}$[/tex]
C. [tex]$66.3 \times 10^{10}$[/tex]
D. [tex]$7.52 \times 10^{11}$[/tex]
Answer (1)
Multiply the coefficients: 6.5
\[\times\] 1.02 = 6.63 .
Multiply the powers of 10: 10^5
\[\times\] 10^6 = 10^{11} .
Combine the results: 6.63
\[\times\] 10^{11} .
The product in scientific notation is \boxed{6.63
\[\times\] 10^{11}} .
Explanation
Understanding the problem We are given the expression (6.5
\[\times\] 10^5)(1.02
\[\times\] 10^6) and we need to find the product in scientific notation. First, we multiply the coefficients and then we multiply the powers of 10.
Multiplying the coefficients Multiply the coefficients: 6.5
\[\times\] 1.02 = 6.63 .
Multiplying the powers of 10 Multiply the powers of 10: 10^5
\[\times\] 10^6 = 10^{5+6} = 10^{11} .
Combining the results Combine the results: 6.63
\[\times\] 10^{11} . This is already in scientific notation, since 1
\[\leq\] 6.63 < 10 .
Examples
Scientific notation is extremely useful in fields like astronomy and physics, where dealing with very large or very small numbers is common. For example, the distance to the nearest star, Proxima Centauri, is approximately 4.017
\[\times\] 10^{13} kilometers. Similarly, the mass of an electron is about 9.109
\[\times\] 10^{-31} kilograms. Using scientific notation makes these numbers easier to handle and compare.
