Which operation could we perform in order to find the number of milliseconds in a year?

• $60\cdot 60\cdot 24\cdot 7\cdot 365$
• $1000\cdot 60\cdot 60\cdot 24\cdot 365$
• $24\cdot 60\cdot 100\cdot 7\cdot 52$
• $1000\cdot 60\cdot 24\cdot 7\cdot 52$

The goal of this question is to convert a year into milliseconds by selecting a suitable formula from the list provided.

For this operation, disregard the use of months in the calculation. They have irregular days, which complicates the operation. Let us start with days, hours, minutes, seconds, and milliseconds. A normal year has $365$ days and one day has $24$ hours, in addition, there are $60$ minutes in an hour and $60$ seconds in a minute.

We need to figure out how many milliseconds there are in a year.

To begin with the solution, milli means thousandth, so one second incorporates $1000$ milliseconds.
$1\, s=1000\, ms$

Following that, there are $60$ seconds in a minute, so the number of milliseconds in one minute can be calculated by multiplying the number of milliseconds in one second by the number of seconds in one minute.

$1\,min=60\,s=1000\cdot60\,ms$

Following this, there are $60$ minutes in an hour, so the number of milliseconds in one hour can be calculated by multiplying the number of milliseconds in one minute by the number of minutes in one hour.

$1\,h=60\,min=1000\cdot60\cdot60\,ms$

Also, a day has $24$ hours, so the number of milliseconds in one day is calculated by multiplying the number of milliseconds in one hour by the number of hours in one day.

$1\,day=24\,h=1000\cdot60\cdot60\cdot24\,ms$

Finally, we make the assumption that a year has 365 days. After that, the number of milliseconds in one year is calculated by multiplying the number of milliseconds in one day by the number of days in one year.

$1\,year=365\,days=1000\cdot60\cdot60\cdot24\cdot365\,ms$

So, from the given options, it can be seen that:

$1000\cdot 60\cdot 60\cdot 24\cdot 365$

is the correct option.

Example $1$

Convert $6$ days and $7$ hours into hours.

Since $1$ day is equal to $24$ hours,

this means $6$ days $7$ hours will be equal to:

$(6\times 24)\,h+7\, h$

$=151\,h$

Example $2$

Convert $2$ years into seconds.

$2$ years is equal to $2(365)=730\, days$

$1$ day is equal to $24\,h$

$1\,h$ is equal to $60$ minutes,

and $1$ minute is equal to $60$ seconds

Hence, $2$ years $= 730 \cdot 24 \cdot 60 \cdot 60 = 63,072,000\,s$