Q:

# Light travels 9.45 \cdot 10^{15}9.45⋅10​15​​ 9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. There are about 3.15 \cdot 10^73.15⋅10​7​​ 3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year.How far does light travel per second?Write your answer in scientific notation.

Accepted Solution

A:
3.00x10^8 meters. If I'm reading this problem correctly, light is traveling at 9.45x10^15 meters per year and that there's 3.15x10^7 seconds per year. So you desire to know the speed of light in meters per second. This is mostly an exercise in handing scientific notion. So we need to divide the total distance that light traveled by the number of seconds. With scientific notation, you divide the significands and subtract the exponents to perform division. So 9.45 / 3.15 = 3 ; Dividing the significands 15 - 7 = 8 ; Subtracting the exponents. So the answer is 3x10^8 meters per second. Since our data has 3 significant figures, the result should also have 3 significant figures, so the final result is 3.00x10^8 meters.