Informative line

# Rounding

• Rounding a number means to change its value slightly.
• It is not as exact as the original value but it is approximately close to the original value.
• Numbers can be rounded to a certain place values like tens, hundreds, thousands etc.

## Rounding off decimal to whole numbers

• To round off a decimal number to a whole number, first analyze the first digit after the decimal point i.e. at the tenths place.

• If the digit at the tenths place is $$5$$ or greater than $$5$$, then the digit at ones place increases by $$1$$ and the digits after the decimal point become zero.

• If the digit at the tenths place is less than $$5$$, the digit at ones place remains same and the digits after the decimal point become zero.

Let's take an example.

Example: Round off $$125.25$$ to the nearest whole number.

• Analyze the first digit after the decimal point i.e. at the tenths place which is $$2$$ and $$2$$ is less than $$5$$.
• Thus, the digit at ones place i.e. $$5$$ remains same and the digits after the decimal point become zero.
• So, the nearest whole number of $$125.25$$ is $$125$$.

#### Round off $$25.700$$ to the nearest whole number.

A $$25$$

B $$26$$

C $$27$$

D $$30$$

×

Analyze $$25.700$$

Here, digit at the tenths place is $$7$$ which is greater than $$5$$.

Thus, the digit at ones place i.e. $$5$$ is increased by $$1$$ ( i.e. $$5+1=6$$) and the digits after the decimal point become zero.

So, the nearest whole number of $$25.700$$ is $$26$$

Hence, option (B) is correct.

### Round off $$25.700$$ to the nearest whole number.

A

$$25$$

.

B

$$26$$

C

$$27$$

D

$$30$$

Option B is Correct

# Rounding Rules for Decimal Number (Hundredths Place)

• To round off the decimal to the nearest tenth's place, analyze the digit after decimal point i.e. at the hundredths place.
• If the hundredths place value is $$5$$ or greater than $$5$$ then digit of tenths place increases by $$1$$ and the digit at hundredths place and thereafter become zero.
• If the hundredths place value is less than $$5$$ then digit of tenths place remains same and the digit at hundredths place and thereafter becomes zero.

Rounding off decimal (hundredths place):

• Let's take an example to understand it.

Example (1): $$49.38$$

• Let's use place value chart.
 Tens Ones Tenths Hundredths 4 9 . 3 8
• In place value chart analyze the hundredths place.
• Here, the digit at the hundredths place is $$8$$ and $$8$$ is greater than $$5$$.
• Thus, the digit of tenths place increases by $$1$$ and the digit at the hundredths place become zero.
• So, the nearest tenths to $$49.38$$ after round-off is $$49.4$$.

Example (2): $$33.42$$

• Let's use place value chart.
 Tens Ones Tenths Hundredths 3 3 . 4 2
• In place value chart analyze the hundredths place.
• Here, the digit at the hundredths place is $$2$$ and $$2$$ is less than $$5$$.
• Thus, the digit at tenths place remains same and the digit at the hundredths place become zero.
• So, the nearest tenths to $$33.42$$ after round-off is $$33.4$$.

#### What is the round off value of $$56.37$$ up to the tenths place?

A $$56.4$$

B $$57.0$$

C $$56.3$$

D $$56.0$$

×

Place value chart for given decimal number is

 Tens Ones Tenths Hundredths 5 6 . 3 7

Here, the digit at the hundredths place is $$7$$ which is greater than $$5$$.

So, the digit at the tenths place is increased by $$1$$.

The digit at the hundredths place becomes zero.

So, the nearest tenths to $$56.37$$ after round off is $$56.4$$.

Hence, option (A) is correct.

### What is the round off value of $$56.37$$ up to the tenths place?

A

$$56.4$$

.

B

$$57.0$$

C

$$56.3$$

D

$$56.0$$

Option A is Correct

# Rounding Rule for Decimal Number (Thousandths Place)

• To round off a decimal to the nearest hundredth place, analyze the digit at the thousandths place.
• If the digit at the thousandths place is $$5$$ or greater than $$5$$ , then the digit at the hundredth place increases by $$1$$ and the digits at the thousandth place and thereafter become zero.
• If the digit at the thousandths place is less than $$5$$ , then the digit at hundredth place remains same and the digits at the thousandth place and thereafter become zero.

Rounding off Decimal Number (Thousandths place):

Rounding up to hundredths place or thousandths place is similar to tenth place. Let's look at an example to understand it.

Example: $$23.759$$

Let's use the place value chart.

 Tens Ones Tenths Hundredths Thousandths 2 3 . 7 5 9
• Analyze the digit at the thousandths place in the given decimal number.
• Here the digit at the thousandths place is greater than $$5$$
• Thus, the digit at the hundredths place increases by $$1$$ and the digit at the thousandth place becomes zero.
• So, the nearest hundredths to $$23.759$$ after round off is $$23.76$$.

• So, the nearest hundredths to $$23.759$$ after  round off is $$23.76$$ .

#### What is the round off value of $$28.39173$$ up to hundredth place?

A $$28.38$$

B $$28.391$$

C $$28.3$$

D $$28.39$$

×

Place value chart for given decimal number is

 Tens Ones Tenths Hundredths Thousandths Ten thousandths Millionths 2 8 . 3 9 1 7 3

Analyze the place value chart.

Here, the digit at the thousandths place is $$1$$ which is less than $$5$$.

Thus, the digit at the hundredths place i.e. $$9$$ remains same and the digits at the thousandths place and thereafter are removed.

So, the nearest hundredth of $$28.39173$$ after round off is $$28.39$$.

Hence, option (D) is correct.

### What is the round off value of $$28.39173$$ up to hundredth place?

A

$$28.38$$

.

B

$$28.391$$

C

$$28.3$$

D

$$28.39$$

Option D is Correct

# Rounding off simple Fraction

Rounding off fraction to the nearest half

• To round off a fraction to the nearest whole number or nearest half, analyze the numerator and the denominator.
• We have three main values to round to $$0$$$$\dfrac{1}{2}$$ , $$1$$, when we round a fraction to the nearest half.
• We round the fraction to whichever half, it is closest.
• If the numerator is almost as large as the denominator round the number up to the next whole number.
• If the numerator is about half of the denominator round the fraction to $$\dfrac{1}{2}$$.
• If the numerator is equidistant from both the nearest half then round the fraction up.

Example: $$\dfrac{7}{8}$$

The numerator $$7$$ is almost as large as the denominator $$8$$, so we shall round off it up to $$1$$.

Example: $$\dfrac{3}{5}$$

The numerator $$3$$ is about half of the denominator $$5$$, so round the fraction to $$\dfrac{1}{2}$$.

#### What is the round off value of $$\dfrac{13}{20}$$?

A $$0$$

B $$1$$

C $$\dfrac{1}{2}$$

D $$2$$

×

Analyze the fraction $$\dfrac{13}{20}$$.

The numerator $$13$$ is about half of the denominator $$20$$.

$$\dfrac{13}{20}$$ is closest to $$\dfrac{1}{2}$$.

So, $$\dfrac{13}{20}$$ becomes $$\dfrac{1}{2}$$.

Hence, option (C) is correct.

### What is the round off value of $$\dfrac{13}{20}$$?

A

$$0$$

.

B

$$1$$

C

$$\dfrac{1}{2}$$

D

$$2$$

Option C is Correct

# Rounding off Mixed Number to Nearest Whole Number

• A mixed fraction or a mixed number lies between two nearest whole numbers.
• A mixed fraction includes both whole numbers and a fraction.
• To round off the mixed fraction to the nearest whole number, analyze the mixed fraction.
• We need to figure out whether a fraction is larger than $$\dfrac{1}{2}$$ or less than $$\dfrac{1}{2}$$.

$$\to$$ If the fraction part of mixed fraction is greater than or equal to $$\dfrac{1}{2}$$, then the fraction is round-up.

$$\to$$ If the fraction part of mixed fraction is less than $$\dfrac{1}{2}$$ then the fraction is round-down.

Example: (i) $$1\dfrac{2}{3}$$

• In this mixed fraction, the fraction part $$\dfrac{2}{3}$$ is greater than $$\dfrac{1}{2}$$ i.e. $$\dfrac{2}{3}>\dfrac{1}{2}$$
• So, mixed fraction $$1\dfrac{2}{3}$$ is round up to nearest whole number i.e. $$2.$$

(ii) $$15\dfrac{1}{4}$$

• In this mixed fraction, the fraction part $$\dfrac{1}{4}$$ is less than $$\dfrac{1}{2}$$ i.e. $$\dfrac{1}{4}<\dfrac{1}{2}$$
• So, mixed fraction $$15\dfrac{1}{4}$$ is round down to nearest whole number i.e.$$15.$$

#### What is the round off value of $$4\dfrac{6}{7}$$?

A $$4$$

B $$5$$

C $$6$$

D $$7$$

×

Given: $$4\dfrac{6}{7}$$

Fraction $$\dfrac{6}{7}$$ is greater than $$\dfrac{1}{2}$$ i.e. $$\dfrac{6}{7}>\dfrac{1}{2}$$

$$\dfrac{6}{7}$$ is closest to $$1$$.

So, $$4\dfrac{6}{7}$$ becomes $$5$$.

Hence, option (B) is correct.

### What is the round off value of $$4\dfrac{6}{7}$$?

A

$$4$$

.

B

$$5$$

C

$$6$$

D

$$7$$

Option B is Correct