Question

a certain star is 2.5×10^2 light - years from the earth. one light - year is about 5.9×10^12 miles. how far from the earth (in miles) is the star? (use scientific notation. use the multiplication symbol in the math palette as needed.) the star is miles from earth.

Explanation:

Step1: Identify given values

The star is $2.5\times 10^{2}$ light - years away and 1 light - year is about $5.9\times 10^{12}$ miles.

Step2: Set up multiplication

We multiply the number of light - years by the number of miles per light - year: $(2.5\times 10^{2})\times(5.9\times 10^{12})$.

Step3: Multiply coefficients

$2.5\times5.9 = 14.75$.

Step4: Add exponents

Using the rule $a^{m}\times a^{n}=a^{m + n}$, we have $10^{2}\times10^{12}=10^{2 + 12}=10^{14}$.

Step5: Write in scientific notation

$14.75\times 10^{14}=1.475\times 10^{1}\times10^{14}=1.475\times 10^{15}$.

Answer:

$1.475\times 10^{15}$