Look Before You Leap!

Class 7 Maths · Chapter 12: Another Peek Beyond the Point · NCERT Ganita Prakash section P2 4.4

Learn

The Earth takes 365.2422 days to go round the Sun, but our calendar year has 365. The extra 0.2422 day seems tiny, yet after 100 years it adds up to 0.2422 × 100 = 24.22 days: the seasons would slowly drift away from the calendar!

0.2422 × 100 = 24.22

Fix 1: add a day every 4th year (a leap year). Four calendar years then have 4 × 365 + 1 = 1461 days, close to 4 × 365.2422 = 1460.9688. But 100 years now have 100 × 365 + 25 = 36,525 days, while the Earth needs 36,524.22: we overcorrected.

100 × 365 + 25 = 36,525

Fix 2: century years (divisible by 100) are not leap years. Now 100 years have 24 × 366 + 76 × 365 = 36,524 days. Over 1000 years that is 3,65,240 days, against 1000 × 365.2422 = 3,65,242.2: still 2.2 days short.

24 × 366 + 76 × 365 = 36,524

Fix 3: a century year divisible by 400 is a leap year after all. So 2000 was a leap year, but 1900 and 2100 are not. Tiny decimals, multiplied over centuries, decide how our calendar works!

2000 leap · 1900, 2100 not leap

Explore: leap or not?

1. Sort the years using all three rules.

Remember

• A year is 365.2422 days, so the calendar needs leap years to keep up.
• Leap year: divisible by 4, but century years only if divisible by 400.

Quick check

How many days does the Earth take to go round the Sun 4 times?

1. 1460.9688
2. 1461
3. 1460
4. 1464.9688

Think about it

With all three rules, how many days are in 400 calendar years? How close is that to 400 × 365.2422?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.