Question

About how many years is \[1000\] days?

Answer 1

Hint:
In the given question, we have been given a number of days. We have to convert them to years. To do that, we divide the number of days by the number of days in a year. Then, if we get a remainder, we divide the remainder by the number of days in the quantity just less than year – month. That will give us the answer in years and months. Then we convert the months to years, and we will get the answer.

Formula Used:
Number of days in a year \[ = 365\]
Number of days in a month \[ = 30\]
Number of months in a year \[ = 12\]

Complete step by step solution:
The given number of days, \[d = 1000\]
We have to convert it to years.
We know, number of days in a year \[ = 365\]
So, we divide \[1000\] by \[365\] and see if we have a remainder.
\[365\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ }}1000\\\dfrac{{ - 730}}{{{\rm{ }}270}}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ }}1000\\\dfrac{{ - 730}}{{{\rm{ }}270}}\end{array}}}}
\limits^{\displaystyle\,\,\, 2}\]
So, we have \[2\] years and \[270\] days.
Now, we convert days to months.
Number of days in a month \[ = 30\]
\[30\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ }}270\\\dfrac{{{\rm{ }}270}}{0}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ }}270\\\dfrac{{{\rm{ }}270}}{0}\end{array}}}}
\limits^{\displaystyle\,\,\, 9}\]
So, we have \[2\]years and \[9\] months.
Now, we convert months to years.
Number of months in a year \[ = 12\]
Hence, \[9\] months \[ = \dfrac{9}{{12}} = \dfrac{3}{4}\] years
So, in total we have \[2\dfrac{3}{4}\] years.

Hence, \[1000\] days is equal to \[2\dfrac{3}{4}\] years.

Note:
In the given question, we had to convert \[1000\] days to years. To solve that, we first divided the number of days by the number of days in a year. Then, since it gave a remainder, we divided the remainder by the number of days in a month. That gave us the answer in years and months. Then we converted the months to years. And that gave us the answer.