Question

light travels 3×10^5 kilometers in one second. how far does it travel in 6.7 seconds? write your answer in scientific notation.

Explanation:

Step1: Recall the distance - speed - time formula

Distance = Speed×Time. The speed of light is $3\times 10^{5}$ km/s and the time is $t = 6.7$ s.

Step2: Calculate the distance

$d=(3\times 10^{5})\times6.7$. First, calculate $3\times6.7 = 20.1$. Then, using the rule of exponents for multiplication $a^{m}\times a^{n}=a^{m + n}$ (here $a = 10$), we have $d=20.1\times 10^{5}$.

Step3: Convert to scientific notation

Scientific notation is of the form $a\times 10^{n}$ where $1\leqslant a<10$. Rewrite $20.1\times 10^{5}$ as $2.01\times 10^{1}\times10^{5}$. Using the exponent - multiplication rule again, $d = 2.01\times10^{1 + 5}=2.01\times 10^{6}$ km.

Answer:

$2.01\times 10^{6}$