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,

$\dfrac{1}{{86400}}$

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

 $ = \dfrac{1}{{8.64 \times {{10}^4}}}$

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

 $ = \dfrac{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,

$\dfrac{x}{1} = \dfrac{1}{{86400}}$

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.