
There are 86,400 seconds in a day. How many days long is a second? Express your answer in scientific notation.
Answer
509.4k+ views
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.
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.
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