light travels $3 \\times 10^5$ kilometers in one second. how far does it travel in 6.7 seconds? write your…

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})