Dustin computed his family's road trip as $4.43 \times 10^3$ miles. How many miles did Dustin's family travel on the road trip?
The given road trip distance is expressed in scientific notation as \(4.43 \times 10^3\) miles. Scientific notation is a way to represent very large or very small numbers as a product of a number (between 1 and 10) and a power of 10. In the expression \(4.43 \times 10^3\), the base number is \(4.43\) and the exponent of 10 is \(3\).
To convert a number from scientific notation of the form \(a \times 10^n\) to standard decimal form, we multiply \(a\) by \(10^n\). Multiplying by \(10^n\) where \(n\) is a positive integer is equivalent to moving the decimal point \(n\) places to the right. In this case, \(n = 3\), so we need to shift the decimal point in \(4.43\) three places to the right.
Starting with \(4.43\), we shift the decimal point three places to the right:
Thus, \(4.43 \times 1000 = 4430\). The distance of the road trip in standard decimal form is \(4430\) miles.
Scientific notation is frequently used by scientists and engineers to express very large or small measurements, such as the distance between planets or the size of microscopic particles. For example, the distance from the Earth to the Sun is approximately \(1.496 \times 10^8\) km. Understanding how to convert between scientific notation and standard form allows for easier comparison and interpretation of these massive physical scales in everyday scientific contexts.