Year in Math

What Is a Year?

A year is the time taken by Earth to make one revolution around the Sun. A year can also be described as a period of 12 months (365 days or 366 days), starting from the first of January and ending on the thirty-first of December.

One complete calendar year can also be expressed as

• This year’s 4th of July to the next year’s 4th of July
• This year’s Christmas day to the next year’s Christmas day
• Your last birthday to your next birthday

Year Definition

A year is the time taken by the earth to make one revolution around the sun. It is the period of 12 months measured from any particular date. 

Ordinary Year and Leap Year

How many days are there in a year? We will discuss this for two cases. There are two types of years:

• Ordinary Year

An ordinary year has 365 days. 

• Leap Year

Leap year has 366 days. Earth orbits the Sun in 365.25 days on average. The days in a calendar year are typically rounded up to 365. We add a day to our calendar every four years or so to make up for the lost part of the day. That is a leap year, when an extra day is added to the end of the shortest month, i.e., February. Intercalary Day is the name given to this day, usually referred to as Leap Day, February 29.

How Many Months Are There in a Year?

There are 12 months in a year. The names of the months are:

Number of Days in a Year

The first day of the year is 1st January and the last day is 31 December. 

In an ordinary year, there are seven months each having 31 days, 4 months each having 30 days and 1 month having 28 days. 

Number of days in an ordinary year $= (7 \times 31) + (4 \times 30) + (1 \times 28)$

$= 217 + 120 + 28$

$= 365$ days

Number of days in a leap year $= (7 \times 31) + (4 \times 30) + (1 \times 29)$

$= 217 + 120 + 29$

$= 366$ days

Average Weeks in a Year

The duration of the Earth’s complete rotation with regard to the Sun is defined as one day. The Earth rotates about its axis once every 24 hours.

There are 7 days in a week which are as follows:

Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday.

There are 365 or 366 days in a year depending on whether it is an ordinary or leap year.  So, how many weeks are there in a year? Let’s find out.

Number of weeks in an ordinary year $= \frac{365}{7} = 52$ weeks $+ 1$ day

Number of weeks in a leap year $= \frac{366}{7} = 52$ weeks $+ 2$ days

Fun Facts

• In astronomy, a Julian year is a measurement unit of time, which is defined as exactly 365.25 days of 86400 SI seconds each.
• The lunar year consists of twelve full cycles of the phases of the Moon (roughly 354 days).
• The galactic year, which is also known as a cosmic year, is termed as the duration of time required for the Sun to orbit once around the center of the Milky Way Galaxy. 
• A fiscal or financial year is a 12-month period for calculating annual financial statements in businesses and other organizations
• The annual period during which a student attends an educational institution is known as an academic year. It may be divided into semesters or quarters. 
• If today is Monday, it will be again a Monday after 7 days as the 7-day cycle repeats itself. 

How to Check Which Year is a Leap Year

Step 1: Check if the year is divisible by 4.

If it is not, it is not a leap year.

Example: 2017 is not a leap year.

Step 2: If the year is divisible by 4, and also divisible by 100, it is not a leap year.

Example: 2300 is not a leap year.

Step 3: If the year is divisible by 4, and also divisible by 400, it is a leap year.

Example: 1600, 2000 are leap years.

10 years, 100 years, 1000 years

• 10 years make one decade.
• 100 years make one century. Meaning of 100 years can also be described using the word “centennial.” A centenary is the hundredth anniversary of some event.
• 1000 years make one millennium.

The years from 1800 to 1899 are called the nineteenth century.

The years from 2000 to 2099 are called the twenty-first century.

Conclusion

In this article, we learned about a year. A year is a specified period of time having 365 or 366 days. Let’s check out some examples and practice problems.

Solved Examples on Year

1. Arrange the months of the year in the correct order. How many months make a year?

Solution: 

There are 12 months in a year.

The correct order of the months is:

January, February, March, April, May, June, July, August, September, October, November, and December.

2. How many days are there in the first 6 months of an ordinary year?

Solution: 

The first 6 months are: January, February, March, April, May, June.

Number of days in January $= 31$

Number of days in February $= 28$

Number of days in March $= 31$

Number of days in April $= 30$

Number of days in May $= 31$

Number of days in June $= 30$

Number of days in first 6 months $= (3 \times 31) + (2 \times 30) + (1 \times 28) = 93 + 60 + 28$

$= 181$ days

3. Check whether 2070 is a leap year or not.

Solution:

$2070 \div 4 = 517.5$ which means 2070 is not completely divisible by 4. 

So, it is not a leap year. 

4. How many months with 31 days are there in a year?

Solution:

Months having 31 days $=$ January, March, May, July, August, October, December.

Number of months having 31 days $= 6$

5. If today is Saturday, what will be the day after 50 days?

Solution:

Each day of the week is repeated after 7 days.

So, after 49 days, it will be Saturday.

$\therefore$ After 50 days, it will be Sunday.

Practice Problems

Frequently Asked Questions on Year