Question

a spaceship travels at a speed of 3.210^5 meters per second. the spaceship continues at this speed for 4.510^3 seconds. how far does the spaceship travel in that time? standard notation: scientific notation: x 10

Explanation:

Step1: Recall the distance - speed - time formula

Distance \(d = s\times t\), where \(s\) is speed and \(t\) is time. Here, \(s = 3.2\times10^{5}\text{ m/s}\) and \(t=4.5\times 10^{3}\text{ s}\).

Step2: Multiply the numbers and powers of 10

First, multiply the non - exponential parts: \(3.2\times4.5 = 14.4\). Then, use the rule \(a^{m}\times a^{n}=a^{m + n}\) for the powers of 10. So, \(10^{5}\times10^{3}=10^{5 + 3}=10^{8}\). Then \(d=14.4\times10^{8}\).

Step3: Convert to proper scientific notation

In scientific notation, the coefficient should be between 1 and 10. So, \(14.4\times10^{8}=1.44\times10^{9}\) (since \(14.4 = 1.44\times10^{1}\), and \(1.44\times10^{1}\times10^{8}=1.44\times10^{9}\)).

Step4: Convert to standard notation

\(1.44\times10^{9}=1440000000\).

Answer:

Standard notation: \(1440000000\)
Scientific notation: \(1.44\times 10^{9}\)