Rounding Numbers

Rounding a number means reducing the number to a simple number(mainly to a multiple of ten, hundred, thousand etc..) while keeping its value close enough to the original number. In other words, it is nothing but to write down the approximate value of a number in a way that performing operations using the number becomes an easy process. There are several ways to round the numbers. Recall the concept of the place value system.

Consider a number 78. You can round 78 nearest to its tens. When you round 78 to the nearest tens, we get 80.

Why can’t 78 be rounded to 70? There are some rules to be followed when you round the number.

Rules for Rounding

The standard rules followed to round a number are as follows:

First step is to understand which place you are required to round the number. You apply the steps on the digit that follows that place.

You need not round a number which is followed by a 0.

If you want to round a number, which is followed by 1, 2, 3, or 4, then the number has to be rounded down to a number less than that number. For example, 53 can be rounded to the nearest tens, is 50.

If you want to round a number which is followed by 5, 6, 7, 8 or 9, then the number has to be rounded up to the number greater than that number. For example, 57 can be rounded to the nearest tens is 60.

Always Remember!

When you stop at a number less than 5, you will move back to 0; when you stop at number greater than or equal to 5, you will reach to 10.

A number can be rounded to the nearest tens, hundreds, or thousands. Let us consider an example 1349.

Rounding the number to the nearest tens: In the given number, the digit 4 in the tens place is followed by the digit 9. Hence, the number should be rounded up to the nearest tens number to 49. Following the steps mentioned above as 9 is greater than 5, 1349 can be rounded to the nearest tens, which is 1350.

Rounding the number to the nearest hundreds: In the given number, the digit 3 is in the hundreds place, followed by 4. As 4 < 5, the number should be rounded down. 1349 rounded to the nearest hundreds is 1300.

Rounding the number to the nearest thousands: In the given number, the digit 1 is in the thousands place, followed by 3. 3 < 5, hence, the number should be rounded down. 1349 rounded to the nearest thousands is 1000.

 
Example 1: Round the following numbers nearest to tens.
a) 27
b) 43
c) 276
d) 381

Solution: To round the numbers nearest to their tens, look at the digit in the units place.

Example 2: Round the following numbers nearest to hundreds.
a) 468
b) 692
c) 841

Solution: To round the numbers nearest to their hundreds, look at the digit in the tens place.

Example 3: Round the following numbers nearest to tens, hundreds and thousands.
a) 4735
b) 5819
c) 2753
d) 3108

Solution: The given numbers can be rounded as shown in the table below

Rounding numbers is an integral part of our daily lives.

Math Facts

9 is the result of rounding up 2π+e.

17≈12√2 so we can use it to approximate √2

22≈7π thus π≈22/ 7 which is used where a fractional approximation is needed.

 

Mathemagician

George Greenhill proceeded to Christ’s Hospital School, where he received the Thompson Mathematical Gold Medal, and then to St John’s College, Cambridge, in 1866. He was a Pitt Club exhibitioner, then a Somerset exhibitioner, a foundation scholar, a London University scholar, and lastly a Whitworth engineering scholar there. In the final examinations of 1870, he was ranked Second Wrangler and shared the Smith’s Prize with R Pendlebury, the First Wrangler.
 

Greenhill specialized in elliptic functions. Their applications to dynamics, hydrodynamics, elasticity, and electrostatics piqued his interest.
Greenhill’s investigation of the maximum length a cylinder can have before it bends under its own weight was a significant contribution to the theory of elasticity. Calculating the greatest height a tree may reach was one of his applications.