Hi,
Qyestion
Convert 10!seconds into weeks?
Please show simplified working as I have to explain it to my 10 year old daughter as it has come up in her exam for 11+
Thanks
Dee
I don't think you meant 10 factorial, so I'll just assume you meant 10 seconds.
1 week is equivalent to 7 days
1 day is equivalent to 24 hours
1 hour is equivalent to 60 minutes
1 minute is equivalent to 60 seconds
$\displaystyle \begin{aligned}
1~\text{week} &= 7~\text{days} \\
&= 7\times 24~\text{hours} \\
&= 7\times 24 \times 60~\text{minutes} \\
&= 7\times 24 \times 60 \times 60~\text{seconds} \\
&= 604800~\text{seconds}\end{aligned}$
But 1 week = 10(60480) seconds and if divided by 60480, we get $\displaystyle 10~\text{seconds} = \frac{1}{60480}~\text{of a week}$
$\displaystyle 10!\ \mathrm{seconds}=10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\ \mathrm{seconds}$
Now there are $\displaystyle 60 \times 60 \times 24 \times 7 $ seconds in a week (that is 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 7 days in a week).
So:
$\displaystyle 10!\ \mathrm{seconds}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{60 \times 60 \times 24 \times 7 } \ \mathrm{weeks}$
Now cancel as many common factors as you can and you should be left with something easy to evaluate.
.