Question

light travels at an approximate rate of 1.9×10^5 mi/sec. there are about 3.2×10^7 seconds in a year. about how many miles does light travel in a year? write the answer in scientific notation. express the answer to the exact decimal place. (1 point)

Explanation:

Step1: Recall distance - rate - time formula

Distance = Rate×Time

Step2: Substitute given values

The rate of light is $1.9\times 10^{5}$ miles per second and the time is $3.2\times 10^{7}$ seconds. So, Distance = $(1.9\times 10^{5})\times(3.2\times 10^{7})$

Step3: Use the properties of exponents

$(a\times 10^{m})\times(b\times 10^{n})=(a\times b)\times10^{m + n}$. Here, $a = 1.9$, $b=3.2$, $m = 5$ and $n = 7$. Then $(1.9\times3.2)\times10^{5 + 7}$

Step4: Calculate the product of the non - exponential parts

$1.9\times3.2=6.08$

Step5: Simplify the exponent part

$10^{5 + 7}=10^{12}$

Answer:

$6.08\times 10^{12}$ miles