Question

There are 86,400 seconds in a day. How many days long is a second? Express your answer in scientific notation.

Answer 1

Hint: We are given the seconds in a day. We can find how long a second is by taking the reciprocal. Then we can convert it to exponential form to express it in scientific notation.

Complete step by step solution: The number of seconds in a day is given as 86400.

Then the days in a second is given by the reciprocal of the seconds in a day. By taking the reciprocal of 86,400 is given by,

${\displaystyle \frac{1}{86400}}$

We can 86400 as power of 10. So we get,

 $={\displaystyle \frac{1}{8.64\times {10}^4}}$

Now we can take the power of 10 to the numerator. So we get,

 $={\displaystyle \frac{1}{8.64}}\times {10}^{-4}$

Now we can do the division. So we get,

$=0.1157\times {10}^{-4}$

To make it in the standard form, we can write as,

$=1.157\times {10}^{-5}$

Thus a second is $1.157\times {10}^{-5}$days long.

Note: Alternate method of approach to this problem is

Let us assume x as the days in a second. We are given that in a day, there are 86,400 seconds.

So by proportionality, we can write as,

${\displaystyle \frac{x}{1}}={\displaystyle \frac{1}{86400}}$

On doing the calculations we get,

$x=0.00001157$

After converting it into exponential form we get,

$x=1.157\times {10}^{-5}$

Therefore a second is $1.157\times {10}^{-5}$days long.