Question

light travels $3 \times 10^5$ kilometers in one second. how far does it travel in 6.7 seconds? write your answer in scientific notation. \boxed{} kilometers

Explanation:

Step1: Recall the formula for distance

Distance \( d \) is equal to speed \( v \) multiplied by time \( t \), i.e., \( d = v\times t \). Here, the speed of light \( v = 3\times 10^{5}\) km/s and time \( t = 6.7\) s.

Step2: Multiply the speed and time

Substitute the values into the formula: \( d=(3\times 10^{5})\times6.7\). First, multiply the coefficients \( 3\times6.7 = 20.1\). Then, keep the power of 10 as \( 10^{5}\) for now, so we have \( 20.1\times 10^{5}\).

Step3: Convert to scientific notation

Scientific notation requires the coefficient to be between 1 and 10. So, we rewrite \( 20.1\times 10^{5}\) as \( 2.01\times 10^{1}\times 10^{5}\). Using the rule of exponents \( a^{m}\times a^{n}=a^{m + n}\), we add the exponents: \( 1+5 = 6\). So the distance is \( 2.01\times 10^{6}\) kilometers.

Answer:

\( 2.01\times 10^{6}\)