Estimating is playing a vital role in mathematics. It has also become a handy tool in our everyday life. In everyday life, we have to estimate the length of time and lots of other physical quantities. Rounding off is one of the most important kinds of estimating. To round off a number means that we will have to make a number simpler. This simpler number should be very close to the actual number. No doubt, the result of rounding off is less accurate. Anyhow, it is easy for us to use the results of the rounding off numbers. For example, if we have a digit 83, it's rounding off value should be 80. Here, we will try to learn round off rules for decimals and whole numbers.

## Round off Rules for Decimals

We have to round off decimals, not in
mathematics but also other fields of life. If you want to round off decimals,
you will have to follow some rules. The basic rules to round off decimals are
given below;

1.
First of all, you
will have to decide the place value that you want to round off. We call this
place value as the rounding digit. After deciding the rounding digit, you
should look at the right digit of this rounding digit.

2.
If the digit at
the right side of the rounding digit is less than 5, you should not change the
rounding digit. Anyhow, you will have to drop all the digits that are present
to the right of the rounding digit.

3.
If the digit at
the right side of the rounding digit is greater than 5, you will have to add
‘1’ in the rounding digit. Just like the previous step, you will have to drop
all the digits that are present to the right of the rounding digit.

4.
In some cases,
the rounding digit can also be equal to 5. If the rounding digit is equal to 5,
you will have to add one in the rounding digit. You should also drop all the
digits that are present to the right of the rounding digit.

## Explanation of Round Off Rules for Decimals with Examples

After understanding the rules to round
off decimals, you can easily round off the decimals. Here, we will try to
explain this concept by solving examples. Round off the following decimals;

A.
4.7871

B.
3.1239

C.
7.1251

We will try to round off these
decimals nearest to tenth place after the decimal point. First of all, we will
try to solve the first example.

4.7871

In this example 4.7871, 8 is the rounding digit. On the ride side of the
rounding digit of this example 4.7871, the digit
is 7. As this digit is greater than 5, therefore, we will have to add one in
the rounding digit. After removing the other digit, the example 4.7871 will
become 4.79.

3.1239

2 is the rounding digit in this
example 3.1239. 3 is the next digit on the right
side of the rounding digit of this example 3.1239.
As it is less than 5, therefore, we don’t need to add one in the rounding
digit. After rounding off, its answer will become 3.12.

7.1251

Here, 2 is the rounding digit in this
example 7.1251. On the right side of the
rounding digit of this example 7.1251, the next
digit is 5. That’s why we will have to add one in the rounding digit. The
answer to this example will be 7.13.

Difference
between Rational and Irrational Numbers

## Round off Rules for Whole Numbers

In some cases, we have to round off
the whole numbers. To round off the whole numbers, we will have to follow some
rules. Here, we will follow the following rules to round off whole numbers.

1.
To round off the
whole numbers, first of all, we will have to find the place value of the digit
that we want to round off. This digit is also known as rounding digit. After
finding the rounding digit, we will have to look at the digits that are at the
right side of the rounding digit.

2.
If the digit
right to the rounding digit is less than 5, we should not add anything in the
rounding digit. Anyhow, we will have to change all the digits right to rounding
digit. We will have to change these digits with zeros.

3.
If the digit
right to the rounding digit is greater than 5, we will have to add one in the
rounding digit. After adding one in the rounding digit, we will have to change
all the digits with the zeros.

4.
Now, if the digit
right to the rounding digit is equal to 5, we should also add one in the
rounding digit. Just like the other two steps, we should also change the
remaining digit right to the rounding digit with zeros.

## Examples of Rounding Off Whole Numbers

After understanding the rules for
rounding off whole numbers, we can easily solve the questions relevant to the
whole numbers. Round off the following whole numbers;

A.
4253

B.
3248

C.
4387

To solve these examples, first of all,
we should try to find the rounding digit. We are going to round off these whole
numbers in the tenth place.

4253

In this example 4253, 2 is the rounding digit. The digit to the right
of the rounding digit in this example 4253 is 5. According to the
rounding off rules, we will have to add one in rounding digit and we will have
to replace all the other digits with zeros. After rounding off, this number
will become 4300.

3248

In the example 3248, 2 is the rounding digit. After the rounding
digit, the next digit is 4. As it is less than 5, therefore, we should not add
one in the rounding digit. After rounding off, its solution will be 3200.

4387

3 is the rounding digit in the example
4387. Now, we will have to look at the digit at
the right side of the rounding digit. In the example of 4387, 8 is the next digit. As it is greater than five,
therefore, we will have to add one in the rounding digit. The solution to this
example will be 4400.

## Everyday Uses of Rounding Off Numbers

While learning mathematical concepts,
most of the people don’t know their uses in everyday life. If you are learning
rules to round off numbers, you should know that there are various uses of the
rounding off numbers in the everyday life. Here, we will explain some uses of
the rounding off numbers in everyday life.

1.
After learning
these rules, you can handle the mismatch between the fractions and decimals.
For example, after dividing a fraction, if we get the answer 0.666666..., we
will have to round off this answer. Its reason is that we will have to work
with only two or three digits only.

2.
You can also
apply these rules to change the multiplied results. For example, if we multiply
0.25 with 0.75, the answer will be 0.1875. If you want to work with just two
points after the decimal point, its answer will be 0.19.

3.
It is also the
best way to find out the value of the sales tax. While buying various things
from the shop, it will be difficult for us to pay tax in decimals. When we will
apply the round off rules, we can easily get the exact value.

4.
You can also use
these rules to do calculations in your mind. To do calculations in your mind,
you will have to find the nearest value of different things.

5.
If we want to
remember 8,213,409, it will be difficult for us. After applying the round off
rules, we can easily remember it. After rounding off, we can read it as 8
million.

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