Informative line

Estimation Of 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.
  • 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 \(2,000\).

Illustration Questions

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 \(30,000\).

Illustration Questions

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.

Illustration Questions

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 ?

image
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 \(400\).

Illustration Questions

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

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