Rounding numbers: Explained with definition, rules, and examples

Rounding number is used to minimize the number of digits and it is used to write a big value in just 3 - 4 digits after a point by applying a condition of greater or equal to 5 then it stops the digit by adding one in its predecessor digit.

It is used for real numbers, and also for decimals at different places of hundreds, tens, and tenths. It is used to preserve the number like significant figures. The number of significant figures is simply the number of figures that are known with some degree of definition.

Number 16.23 is said to have 4 significant figures. As you know the definition of a significant figure non-zero digits are always significant. 3.67875 has six significant digits (all digits have useful information). Thus, 6.9 has two significant digits.

Moreover, in this article, methods of rounding off numbers nearest tenths, hundreds, thousands, or ten thousand and their benefits, and the way to round off the number in the respective category like real numbers and decimals.

Definition of round off

“It is defined as the number is made easier for calculation by balancing its overall value but nearest tenths, hundredths, and thousands and so on.”

Types of rounding off the number

There are two types of rounding-off numbers.

a)     Rounding up                               b) Rounding down

a)   Rounding up

Rounding up means if the number you are rounding has followed by 5 or greater than 5 then add +1 to its predecessor and after that number, all digits become zero. For Example, 77 is rounded to 80 nearest ten.

b)  Rounded down

Rounding up means if the number you are rounding has followed by less than 5 then after that number all digits become zero. For Example, 64.2342 is rounded to 64.2

Rules of rounding off

1.   Rounding off to the nearest 10

Round off to the nearest 10 will be discussed here. It will be done for every place value of a number. Now to round off a number to its nearest tens, we round off to the nearest multiple of ten.

Rule 1:

Rounding off to the nearest ten see if the digit in the unit place means in ones is between 0 – 4 or less than 5 then the unit digit is simply replaced by a number 0.

Rule 2:

While if the digit in ones is 5 to 9 or 5 but less than 10, then the unit place is simply replaced by ‘0’, and the tens place is increased by +1.

2.   Rounding off to the nearest 100

Round off to the nearest 100 will be discussed here. To round off a number to its nearest hundreds, we round off to the nearest multiple of hundreds.

Rule 1:

Rounding off to the nearest hundred see if the digit in the tens place is between 0 – 4 or less than 5 then the tens place is simply replaced by a number 0.

Rule 2:

While if the digit in ones is 5 to 9 or 5 but less than 10, then the tens place is simply replaced by ‘0’, and the hundreds place is increased by +1.

3.   Rounding off to the nearest 1000

Round off to the nearest 1000 will be discussed here. To round off a number to its nearest thousands, we round off to the nearest multiple of thousands.

Rule 1:

Rounding off to the nearest thousands see if the digit in the hundreds place is between 0 – 4 or less than 5 then the hundreds place is simply replaced by a number 0.

Rule 2:

While if the digit in the hundreds place is 5 to 9 or greater than 5 then the hundreds place is simply replaced by ‘0’ and the thousands place is increased by +1.

Try a rounding calculator to round off the given number according to the above rules.

 

Examples section

In this section of examples, rounding off to tens, hundreds and thousands will be performed one by one. A round off calculator can also be used to solve the numerical problems of rounding numbers to nearest tens, hundred, and thousands.

Section 1

In this section rounding off to the nearest 10 will be discussed.

Example 1

Round off 67 to the nearest 10

Now see the digit in unit place is greater than 5 now ones place convert it in ‘0’ and the tens place can be increased by 1. So, it becomes 70 which is its nearest multiple of 10.

Example 2

Round off 33 to the nearest 10

The digit in unit place is less than 5 now one place converts into ‘0’. So, it becomes 30 which is its nearest multiple of 10.

Section 2

In this section rounding off to the nearest 100 will be discussed.

Example 1

Round off 663 to the nearest 100

Now see the digit in the tens place which is greater than 5 now the tens place convert into ‘0’ and the hundred places can be increased by 1. So, it becomes 700 which is its nearest multiple of 100.

Example 2

Round off 440 to the nearest 100

The digit in unit place is less than 5 now tens place is converted into ‘0’. So, it becomes 400 which is its nearest multiple of 100.

Section 3

In this section rounding off to the nearest 1000 will be discussed

Example 1

Round off 7783 to the nearest 1000

Now see the digit in the hundred places which are greater than 5 now hundred places will convert to ‘0’ and thousands of places can be increased by 1. So, it becomes 8000 which is its nearest multiple of 1000.

Example 2

Round off 3250 to the nearest 1000

The digit in the hundred places is less than 5 now hundreds of places convert into ‘0’. So, it becomes 3000 which is its nearest multiple of 1000.

Summary

In this article, the detail of rounding-off numbers is discussed with a basic definition, methods, and rules for rounding off a number with their types and rounding off to nearest tenths, hundredths, and thousandths with explanations and examples discussed in this article. 

Moreover, after reading this article, you can easily round off the numbers to the nearest tenths, hundredths, and thousandths to make the calculation easier.