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 Rules: The rules which are used to change the number to the nearest power of ten are known as rounding rules.

## Rounding rules for thousands place

• To round off a whole number to the nearest thousands place, analyze the digit at the hundreds place.

• If the digit at the hundreds place is $$5$$ or greater than $$5$$, then round the number up to the nearest thousands place.
• If the digit at the hundreds place is less than $$5$$, then round the number down to the nearest thousands place.

Let's take an example.

Round off the whole number $$1,415$$, to the nearest thousands place.

• We know that the nearest thousands to $$1,415$$ are $$1,000$$ and $$2,000$$.
• Hundreds place digit $$4$$, is less than $$5$$ and also $$1,415$$ is closer to $$1,000$$ than to $$2,000$$.
• So, we will round the number down to $$1,000$$.

Note: The values from $$1,001$$ to $$1,499$$ are rounded down to $$1,000$$ and the values from $$1,500$$ to $$1,999$$ are rounded up to $$2,000$$.

#### Round off the number: $$2,875$$

A $$3,000$$

B $$2,000$$

C $$1,000$$

D $$4,000$$

×

Given: $$2,875$$

The nearest thousands to $$2,875$$ are $$2,000$$ and $$3,000$$.

Hundreds place digit $$8$$, is greater than $$5$$ and also $$3,000$$ is closer to $$2,875$$.

So, we will round the number up to $$3,000$$.

Hence, option (A) is correct.

### Round off the number: $$2,875$$

A

$$3,000$$

.

B

$$2,000$$

C

$$1,000$$

D

$$4,000$$

Option A is Correct

# Rounding Rules for Ten-thousands Place

• To round off a whole number to the nearest ten-thousands place, analyze the digit at the thousands place.

• If the digit at the thousands place is $$5$$ or greater than $$5$$, round the number up to the nearest ten-thousands place.

• If the digit at the thousands place is less than $$5$$, round the number down to the nearest ten-thousands place.

Let's take an example.

Round off the whole number $$23,750$$ to the nearest ten-thousands place.

• We know that the nearest ten thousands to $$23,750$$ are $$20,000$$ and $$30,000$$.
• Thousands place digit $$3$$ is less than $$5$$ and also $$23,750$$ is closer to $$20,000$$.
• So, we will round the number $$23,750$$ down to $$20,000$$.

Note: The values from $$20,001$$ to $$24,999$$ are rounded down to $$20,000$$ and the value from $$25,000$$ to $$29,999$$ are rounded up to $$30,000$$.

#### Round off the number: $$46,200$$

A $$4,000$$

B $$5,000$$

C $$40,000$$

D $$50,000$$

×

Given: $$46,200$$

The nearest ten-thousands to $$46,200$$ are $$40,000$$ and $$50,000$$.

Thousands place digit $$6$$, is greater than $$5$$ and also $$50,000$$ is closer to $$46,200$$.

So, we will round the number up to $$50,000$$.

Hence, option (D) is correct.

### Round off the number: $$46,200$$

A

$$4,000$$

.

B

$$5,000$$

C

$$40,000$$

D

$$50,000$$

Option D is Correct

# Estimation

• Estimation means finding an answer which is close to the correct answer by doing a rough calculation of the value, number, quantity on an extent of something.
• Estimation is a very easy method to find the answer quick.
• In daily life, estimation is handy tool.
• When we want to find an answer which belongs to our daily life's problem and we don't need an exact answer then we can use estimation method.
• In estimation method, it is important that the answer must make a sense and work with our problem.

Let's take an example to understand estimation.

• A bottle is filled with water as shown in a figure. If someone asks, to what level is the bottle filled , then we can say that half of the bottle is filled with water.
• In this example, we are saying that half bottle is filled, this answer is estimated answer and is working with our problem.

Note: In this example, we don't need to give an exact answer so we can use estimation method.

#### There are two towers, A and B as shown in the figure. Tower A has $$42$$ storeys while tower B has only $$10$$ storeys. The height of tower B is $$32$$ meters. What is the approximate height of tower A ?

A $$30\,m$$

B $$40\,m$$

C $$130\,m$$

D $$60\,m$$

×

As shown in the figure, tower B has $$10$$ storeys while tower A has $$42$$ storeys which is approximately four times.

The Height of tower B is $$32$$ meters, that means height of tower A is approximately $$4$$ times the height of tower B.

Height of tower A $$= 4\times32=128$$

$$=130$$ meters (approximately)

Hence, option (C) is correct.

### There are two towers, A and B as shown in the figure. Tower A has $$42$$ storeys while tower B has only $$10$$ storeys. The height of tower B is $$32$$ meters. What is the approximate height of tower A ?

A

$$30\,m$$

.

B

$$40\,m$$

C

$$130\,m$$

D

$$60\,m$$

Option C is Correct

# Rounding Rule for Whole Numbers

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. A number can be rounded to a certain place values like tens, hundreds, thousands etc.

Rounding Rules:

The rules which are used to change the number to the nearest power of ten are known as Rounding Rules.

Rounding Rules for tens place:

• To round off a 2-digit number or a higher number to the nearest tens place, analyze the digit at the ones place.
• If the digit at ones place of a two-digit number is less than five, then round the number down to the nearest tens place.
• If the digit at ones place of a two-digit number is greater than five, then round the number up to the nearest tens place.

For Example: $$59$$

• When we analyze the number, we find that the nearest tens to $$59$$ are $$50$$ and $$60$$.
• $$9$$ which is at ones place is greater than $$5$$ and also $$59$$ is closer to $$60$$
• So, we will round up the number to $$60$$.

Rounding Rules for hundreds place:

• To round off a whole number to the nearest hundreds place, analyze the digit at the tens place.
• If the digit at the tens place is $$5$$ or greater than $$5$$, round the number up to the nearest hundreds place.
• If the digit at the tens place is less than $$5$$, round the number down to the nearest hundreds place.

For example: $$365$$

• After analyzing the tens place of the number, we see that the nearest hundreds to $$365$$ are $$300$$ and $$400$$. Tens place digit, $$6$$ is greater than $$5$$ and the number $$365$$ is closer to $$400$$.

So, we shall round the number up to $$400$$.

Note:

The values from $$301$$ to $$349$$ are round off to $$300$$ and the values from $$350$$ to $$399$$ are round off to $$400$$.

#### Calculate the round off value of $$575$$.

A $$500$$

B $$600$$

C $$400$$

D $$700$$

×

The nearest hundreds to $$575$$ are $$500$$ and $$600$$.

Tens place digit, $$7$$ is greater than $$5$$ and also $$600$$ is closer to $$575$$.

So, we shall round off to $$600$$.

Hence, option (B) is correct.

### Calculate the round off value of $$575$$.

A

$$500$$

.

B

$$600$$

C

$$400$$

D

$$700$$

Option B is Correct