## Intermediate Algebra for College Students (7th Edition)

$$407,000,000,000 = 4.07\times10^{11}$$
$$407,000,000,000$$ The final form of the expression should be: $a\times10^{n}$. The steps to convert from decimal to scientific notation include: 1. Determine $a$, the numerical factor. Move the decimal point in the given numberto obtain a number whose absolute value is between 1 and 10, including 1. 2. Determine $n$, the exponent on $10^{n}$. The absolute value of $n$ is the number of places the decimal point was moved. The exponent $n$ is positive if the decimal point was moved to the left, negative if the decimal point was moved to the right, and 0 if the decimal point was not moved. In this case, $a=4.07$ since this is the largest number between 1 and 10 that can be obtained from the given expression. In obtaining $4.07$, the the decimal point was moved $11$ places to the left. Following the statement above, $n$ would be positive. Thus, writing this in the form $a\times10^{n}$: $$4.07\times10^{11}$$