Concept 3 of 7
Calendar Sense: Days, Weeks, Months, Leap Years
Today's big idea
Leap year: divisible by 4, BUT not 100, UNLESS also by 400.
Century years are the trap: they need 400, not 4.
How it works
👀 What's going on?
Some months hold 31 days, some hold 30, and February cannot make up its mind. Every fourth year it grows a spare day. Almost every fourth year, anyway.
💡 Here's the trick
Look at the flowchart above. A year is a leap year when 4 divides it exactly. A year ending in two zeros is fussier, because it must divide by 400. So 2000 was a leap year and 1900 was not.
🪄 How to do it
- 1.Read the flowchart above and test whether 4 divides the year.
- 2.If the year ends in two zeros, test 400 instead of 4.
- 3.Give February 29 days in a leap year and 28 days otherwise.
✍️ Try it
Was 1800 a leap year? Then: counting 5 June but not 14 May, how many days is it from 14 May to 5 June?
1800 divides by 4 and by 100, but not by 400, so it was not a leap year. May has 31 days, so 17 days are left after 14 May, and 17 plus 5 gives 22 days.
⚠️ Watch out
You might be thinking every year that 4 divides is a leap year. Years ending in two zeros break that rule. 1900 divides by 4, yet its February held only 28 days.
🌟 Why this matters
Booking a holiday, counting down to a birthday or working out a due date all need day counts. Getting February wrong throws the whole count out by one.
Exam tip: Say whether both end dates are counted, because that alone decides the answer.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Is 1900 a leap year?”
- 1
Check divisibility by 4
1900 ÷ 4 = 475 → YES. 📅
- 2
Check divisibility by 100
1900 ÷ 100 = 19 → YES → exception kicks in.
- 3
Check divisibility by 400
1900 ÷ 400 = 4.75 → NO.
- 4
Verdict ✓
1900 is NOT a leap year (div by 100 but not 400).
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Knuckle trick: Jan Mar May Jul Aug Oct Dec = 31 · Apr Jun Sep Nov = 30 · Feb = 28/29.
CASE · ROUND 1 OF 3
Is 2100 a leap year?
Quick check
✅ VERIFICATION
How many days were there in February 2016?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Temperature
Drop on integer line: 12 → −3 is 15° down.