# ROUNDING DECIMALS - METHODS OF ROUNDING WITH SOLVED EXAMPLES AND EXERCISE

Decimals before Rounding decimals,
if you have not already done so.

The knowledge of decimals and

Decimal Place value chart

are prerequisites here.

In practice, instead of taking the entire part
of the decimal part, we take the approximate value.
we some times take the whole number
nearest to the decimal number.

Some times, we may take the value nearest
to one or two or three or more decimal places.

Depending on the intended purpose, we take
an approximate value of the decimal number.

## Rounding Decimals

The process of obtaining the value of a decimal
correct to the required number of decimal places
is called rounding and the value obtained is called
the rounded or corrected value of the decimal.

### Rounding Decimals to the nearest whole number :

Method :

Step 1 :
Retain all the digits of the whole number
part and omit the decimal part.

Step 2 :
Out of the omitted decimal part, if the first digit
to the right of the decimal point is 5 or more,
then increase the number formed from the retained
digits by 1, otherwise do not make any change.

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### Examples on Rounding Decimals to the nearest whole number

Round off to the nearest whole number.

1. 97.46
2. 23.81
3. 67.54

Solution :
(i) 97.46
We retain the whole number part in 97.46 to get 97
and omit the decimal part .46.

Out of the omitted digits, the first digit to the right of the decimal point is 4 < 5.

So, we do not make any change to the retained whole number.

∴ Required Number = 97 Ans.

(ii) 23.81
We retain the whole number part in 23.81 to get 23
and omit the decimal part .81.

Out of the omitted digits, the first digit to the right of the decimal point is 8 > 5.

So, we increase the retained whole number by 1.

∴ Required Number = 23 + 1 = 24 Ans.

(iii) 67.54
We retain the whole number part in 67.54 to get 67
and omit the decimal part .54.

Out of the omitted digits, the first digit to the right of the decimal point is 5 = 5.

So, we increase the retained whole number by 1.

∴ Required Number = 67 + 1 = 68 Ans.

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### Rounding Decimals to the required number of decimal places

Method :

Step 1 :
Retain as many digits after the decimal point
as are required and omit the remaining digits.

Step 2 :
Out of the omitted decimal part, if the first digit
to the right of the decimal point is 5 or more,
then increase the last retained digit by 1,
otherwise do not make any change.

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### Examples on Rounding Decimals to the required number of decimal places :

Round off

1. 9.1347, correct to 3 decimal places (or to thousandths' place.)
2. 5.732, correct to 1 decimal place (or to tenths' place.)
3. 0.047, correct to 2 decimal places (or to hundredths' place.)

Solution :
(i) 9.1347, correct to 3 decimal places.
We retain 3 digits of the decimal part in 9.1347 to get 9.134
and omit the digit 7.

The first omitted digit is 7 > 5.

So, we increase the last retained
digit (4) by 1 ( i.e. make it 5).

∴ Required Number = 9.135 Ans.

(ii) 5.732, correct to 1 decimal place.
We retain 1 digit of the decimal part in 5.732 to get 5.7
and omit the digits 3 and 2.

The first omitted digit is 3 < 5.

So, we do not make change to the retained digits.

∴ Required Number = 5.7 Ans.

(iii) 0.047, correct to 2 decimal places.
We retain 2 digits of the decimal part in 0.047 to get 0.04
and omit the digit 7.

The first omitted digit is 7 > 5.

So, we increase the last retained
digit (4) by 1 ( i.e. make it 5).

∴ Required Number = 0.05 Ans.

### Exercise on Rounding Decimals

1. Round off to the nearest whole number.
1. 197.351
2. 42.78
3. 231.51
2. Round off
1. 7.6428, correct to 3 decimal places (or to thousandths' place.)
2. 9.157, correct to 1 decimal place (or to tenths' place.)
3. 0.451, correct to 2 decimal places (or to hundredths' place.)

For Answers see at the bottom of the page.

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### Answers to Exercise on Rounding Decimals

Answers to Problems on Rounding Decimals :

1.
1. 197
2. 43
3. 232
2.
1. 7.643
2. 9.2
3. 0.45