Question

the speed of light is 1.86×10^5 miles per second.how many miles will light travel in 4,200,000 seconds?

Answer 1

Answer: $7.812*10^{11}\ miles$

Step-by-step explanation:

Let be "x" the amount of miles light will travel in 4,200,000 seconds.

Rewrite 4,200,000 seconds in Scientific notation. Move the decimal point 6 places to the left. Then:

$4,200,000\ seconds=4.2*10^6\ seconds$

According to the exercise, light travels $1.86*10^5$ miles in 1 second.

Therefore, based on this data, you can set up the following proportion:

$\frac{1.86*10^5\ miles}{1\ second}=\frac{x}{4.2*10^6\ seconds}$

And finally, you must solve for "x" in order to find its value.

(Remember the Product of powers property: $a^m*a^n=a^{mn}$)

Then:

$(4.2*10^6\ seconds)(\frac{1.86*10^5\ miles}{1\ second})=x\\\\x=7.812*10^{11}\ miles$