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In the Gregorian calendar, every year which is divisible by 4 is a leap year, except for years which are divisible by 100; those years are only leap years if they're divisible by 400 . (This may seem complicated, but the calendar is carefully designed to keep the average number of days per year very close to the number of days in one complete orbit of the Earth.)

Assuming we keep using the Gregorian calendar, how many leap years will there be between 2001 and 2999?

Apr 25, 2018

#1
+3

Hey guest.

We first need to find about how many numbers between 2001 and 2999 are divisible by 4.

The largest number between these two values that is still divisible by 4, is 2996.

The largest number between these two values that is still divisible by 4, is 2004.

To find out how many numbers are divisible by 4, we do:

\((2996-2004)\div4+1=249\)

Now we need to see how many of these numbers are divisible by 100.

From 2001 to 2999, we have:

2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, and 2900

Now we need to see how many of these numbers are divisible by 400.

We have:

2400, 2800

Finally, we have:

\(249-9+2=242\)

The answer you seek is 242.

i hope this helped,

Gavin.

Apr 25, 2018

#1
+3

Hey guest.

We first need to find about how many numbers between 2001 and 2999 are divisible by 4.

The largest number between these two values that is still divisible by 4, is 2996.

The largest number between these two values that is still divisible by 4, is 2004.

To find out how many numbers are divisible by 4, we do:

\((2996-2004)\div4+1=249\)

Now we need to see how many of these numbers are divisible by 100.

From 2001 to 2999, we have:

2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, and 2900

Now we need to see how many of these numbers are divisible by 400.

We have:

2400, 2800

Finally, we have:

\(249-9+2=242\)

The answer you seek is 242.

i hope this helped,

Gavin.

GYanggg Apr 25, 2018