Large Numbers

 Mind Maps

Class V - maths: Large Numbers
Q) What is the predecessor of the number 23, 45, 679?

Q) What is the successor of the number 23, 45, 679?

Q) Write the following 52963 in words?

Q) What is the place value of 4 in 32894?

Q) Write the commas at the appropriate places in the following 2792345 to separate the periods?

Q) Numbers are the mathematical representation used to?

Q) Numbers can be compared by?

Q) The greatest number is formed when the digits are arranged in the?

Q) The smallest number is formed if the digits are arranged in the?

Q) Write the Roman numerals for 25 = ?

Q) What is the face value of 4 in 45683?

Q) Write th following LXXX Roman numerals in Hindu-Arabic numerals?

Q) Write the 585 Hindu-Arabic numerals in Roman numerals?

Q) Round off 5550 to the nearest 1000?

Q) Round off 124 to the nearest 100?

Q) Compare 32, 67, 108 and 37, 89, 100?

Q) What is Comparing Numbers?

Q) What is the Number System?

Q) What is the Forming Numbers?

Q) What is Predecessor and Successor?

Q) Compare 2,64,783 And 2,64,129?

Q) Form the greatest and the smallest numbers with the given digits 6, 7, 2, 8, 0, 1?

Q) Write the number name for 83, 45, 02, 148?

Q) Write 7328504 in the expanded form in words?

Q) Compare 27, 35, 63, 603 and 27, 35, 63, 601?

Q) Write the numeral for the Six crore thirty-nine lakh forty four thousand two hundres ninety-six?

Q) Write the face value and place value of 4 in 13, 14, 892?

Q) What is Comparing Numbers and give an example?

Q) What is the Number System and give an example?

Q) What is the Forming Numbers and give an example?

Q) What is Predecessor and Successor? Give an examples?

Q) Find the place value of the digits 32, 46, 123?

Q) Write the number 62198731 and place its digits in the place value chart?

Q) Write the standard form of 60,00,00,000 + 4,00,00,000 + 70,00,000 + 3,00,000 + 20,000 + 1000 + 200 + 40 + 7?

#### Numbers

Numbers are the mathematical representation used to count, measure and label. The basic classification of numbers is: even, odd, and prime numbers. All mathematical operations are based on numbers.
In this chapter we will discuss the larger numbers.
Numbers are classified into different ways.

1.Rounding Off Numbers

The rounding of a number gives the approximate number, rather than the exact number.
Rounding off the number gives a value of the number which is very close to the actual value.
It involves a very simple technique of rounding off the numbers to the nearest 100, 1000 and so on.
Let consider a table to see the rounding off numbers to the nearest 10, 100, and 1000.

There are also some convenient methods for rounding off numbers.
Let us see some of the short-cut methods for rounding off numbers

Round Off A Number To The Nearest 10

• To round off a number to the nearest 10, observe its ones digit.
• If the ones digit is less than 5, replace the ones digit by 0 and retain the other digits.
• If the ones digit is 5 or greater than 5, increase the tens digit by 1, replace the ones digit by 0, and retain the other digits as such.

Round Off A Number To The Nearest 100

*To round off a number to the nearest 100, observe the numbers formed by the tens and ones digits.
* If the number formed by the tens and ones digit is less than 50, replace the tens and ones digit by 0, and retain the other digits.
* If the number formed by the tens and ones digit is 50 or greater than 50, increase the hundreds digit by 1, replace the tens and ones digits by 0, and retain the other digits as such.

Round Off A Number No The Nearest 1000

* To round off a number to the nearest 1000, observe the numbers formed by the hundreds, tens, and ones digits.
* If the number formed by the three digits is less than 500, replace the hundreds, tens, and ones digits by 0 and retain the other digits.
* If the number formed by the three digits is 500 or greater than 500, increase the thousands digit by 1, replace the hundreds, tens, and ones digits by 0, and retain the other digits as such

#### Comparing Numbers

Definition

Numbers can be compared by the place values of the digits in the numbers
The comparison of bigger numbers is similar to the comparison of smaller numbers.
Let us see the rules to compare numbers.

Rules:

1)The number with more digits is greater than the number with less digits.

Example:

4532897 > 624158

2) If two numbers have the same number of digits, we compare them by comparing the digits from the extreme left and continue till two different digits are found.
These digits are compared to decide the greater and smaller numbers.

Examples:

a) Compare 2,64,783 And 2,64,129.

Solution:

As both the numbers have 6 digits, we start comparing the digits from the left most end.
on comparing 2, 64, 783 and 2, 64, 129,we find the digits 2,6 and 4 are common for both the numbers.
But,the digit 7 is greater than 1.

So,we can say that the number:
2, 64, 783 > 2, 64, 129.

b) Compare 67, 42, 804 and 67, 42, 926.

Solution:

As both the numbers are 7- digits numbers. So, we start comparing the digits from the extreme left
on comparing 67, 42, 804 and 67, 42, 926, we find the digits 6,7,4 and 2 are common for both the numbers.
But the digit 8 is less than 9.
So,we can say that the number,67, 42, 804 < 67, 42, 926.

Understanding Face Value And Place Value

Face value:

Face value is the actual value of a digit.

Example:

Let us consider a number 4, 56, 289.
In this number, the face value of 4 is 4, 5 is 5, 6 is 6, 2 is 2 8 is 8 and 9 is 9.
So, we can say that:
The face value of a digit in a number is the value of the digit itself, regardless of its position in the number
If we consider the face value of a number 88,88,88,888.
Here, the face value of each 8 is 8, but the place value of each 8 is different.
Let us arrange this number in the place value chart.

Place value:

The place value of a digit in a number depends upon the place it occupies in the place value chart.
From the place value chart for 88, 88, 88, 888, we can observe the following facts.
The digit 8 in the tens place is 10 times the digit 8 in the ones place.
The digit 8 in the hundreds place is 100 times the digit 8 in the ones place.
The digit 8 in the thousands place is 1000 times the digit 8 in the ones place
The digit 8 in the ten thousands place is 10,000 times the digit 8 in the ones place, and so on...

The Value Of Each Digit Is Ten Times The Value Of The Digit On Its Immediate Right.

Example:
Find the place value of the digits 32, 46, 123.

Solution:

Place value of 3 is 3 × 1 = 3
Place value of 2 is 2 × 10 = 20
Place value of 1 is 1 × 100 = 100
Place value of 6 is 6 × 1000 = 6, 000
Place value of 4 is 4 × 10000 = 40, 000
Place value of 2 is 2 × 100000 = 2, 00, 000
Place value of 3 is 3 × 1000000 = 30, 00, 000

Place Value Chart

The place value chart given below is separated into four groups.
Each group is called a period. So, there are four periods in this place value chart, namely ones, Thousands, Lakhs, and Crores.

#### Different Ways Of Expressing A Number

There are different ways of expressing a number in order to understand correctly.
A number can be expressed for reading, writing in standard and expanded form, and expanded form in words.

Example:

Write the number 62198731 and place its digits in the place value chart.

Solution:

The place value chart helps us to read, write and operate the numbers in various forms.

Six crore twenty one lakh ninety eight thousand seven hundred and thirty one

2) Standard Form:

6, 21, 98, 731.

3)Expanded Form:

6, 00, 00, 000 + 20, 00, 000, + 1,00,000 + 90, 000 + 8000 + 700 + 30 + 1

4)Expanded Form In Words:

6 crores + 2 ten lakhs + 1 lakh+ 9 ten thousands + 8 thousands + 7 hundreds + 3 tens + 1 ones.

Examples:

1.Write the standard form of :

60,00,00,000 + 4,00,00,000 + 70,00,000 + 3,00,000 + 20,000 + 1000 + 200 + 40 + 7

Solution:

By using the place value chart, we get:

The standard form is: 64, 73, 21, 247.

2.Write 2319478 in the expanded form in words

Solution:

23, 19, 478 = 2 ten lakhs + 3 lakhs + 1 ten thousand + 9 thousand + 4 hundreds + 7 tens + 8 ones.

3. Write the number name for 87, 42, 36, 520.

Solution:

87, 42, 36, 520 = Eighty seven crore forty two lakh thirty six thousand five hundred and twenty.

4. Express 5239814 in the expanded form.

Solution:

Insert the commas at the appropriate places and then start from the digit on the extreme left.
52, 39, 814 = 50, 00, 000 + 2, 00, 000 + 30, 000 + 9000 + 800 + 10 + 4.

#### Marking The Periods

Why do we need to mark the periods in a number?
a) Marking periods helps us to read large numbers.
b) Marking periods help us to write numbers Correctly.
c) The place value of a number is worked out easily.
d) By marking the periods, it becomes simple to Compare Numbers

#### 7 - Digit And 8- Digit Numbers

We know that the largest 6-digit numbers is 999999.
When we add 1 to this largest 6-digit number we get the smallest 7-digit number.
Example:
This number 1000000 is read as ten lakh.
Similarly, if we add 1 to this largest 7-digit number, we get the smallest 8-digit number.
Example:
We read 10000000 as 1 crore

The place value chart is used to read and write large numbers.
Numbers are read from left to right. When a number is read, all the digits under the same period are read together and the name of the period is read along with them except ones period
Example:

34, 27, 591 is read as thirty four lakhs, twenty seven thousand, five hundred and ninety one.
21, 69, 347is read as twenty one lakhs, sixty nine thousand, three hundred and forty seven.
6, 31, 59, 726is read as six crores, thirty one lakhs, fifty nine thousand, seven hundred and twenty six.

Writing 7 - Digit And 8- Digit Numbers

Few steps have to be followed to write the 7-digit and 8-digit numbers

Examples:

The number sixty two lakh thirty four thousand two hundred and ninety one can be written as:

1) Form the three periods

2) Write all the entries of lakhs in the first period from the left

3) Write all the entries of thousands in the second period from the left

4) Write the hundred,tens and ones in the third period from the left

5) Insert the commas to separate periods.
So,the number is 62, 34, 291.

6) Forty-six lakh thirty eight thousand two hundred and thirteen

7) Five crore thirty six lakh twenty eight thousand six hundred and twenty two

9-Digit Numbers:

There are numbers beyond 8-digits as natural numbers begin from 1 and naturally go on beyond 8 digits into infinity

Example:

Twelve crore thirty two lakh forty six thousand two hundred and thirty one can be written as:
12, 32, 46, 231

1) Always read from left to right from the highest period to the smallest.
2) Mark the periods
3) Read the digits in a period together

Examples:

The above examples can be read as:
• Thirty one crore, forty six lakh, twenty eight thousand, seven hundred and thirteen
• Sixty four crore, eighteen lakh, sixty nine thousand, two hundred and thirty six.

Writing 9-Digit Numbers

1. Make a place value chart
2. Mark the periods
3. Name the places in each period from right to left.

Example:

Six crore, forty eight lakh thirty six thousand one hundred and two.

Read each period correctly and fill the empty places with a zero.

### Forming Numbers

Definition

We know that, the greatest number is formed when the digits are arranged in the descending order.
Similarly the smallest number is formed if the digits are arranged in the ascending order.
they are two types:
1.Smallest Number
2.Greatest Number

Example:

Form the greatest and the smallest numbers with the given digits: 6, 7, 2, 8, 0, 1.

Solution:

The given digits are 6, 7, 2, 8, 0, and 1.

Greatest Number:

To get the greatest number, we write the digits in the descending order.
So, the required number is 8, 76, 210..

Smallest Number:

To get the smallest number, we write the digits in the ascending order, by putting the zero in the seconds place.
So, the required number is 1, 02, 678.

### The Number System

The number system classified into different types.
They are

1. Roman Numerals
2. Indian System Of Numeration
3. International System Of Numeration
4. Hindu-Arabic Numbers
Roman Numerals

The Roman numeral system is the numeral system of ancient Rome.
It is based on the letters of the English alphabet, which are combined to signify their values.
Roman numerals are mainly used because of their historic importance.
The ancient Romans used the letters arranged from the greatest value to the least value starting from the left.
The basic symbols used by the Romans to write their numerals were 7 letters of the English alphabet.
They are given in the table below with their values in Hindu-Arabic numerals.

The first ten Roman Numerals are:

Rules For Reading And Writing Numbers:

1. symbol can be repeated a maximum of three times.
2. only I, X, C, A and M can be repeated.
3. If one or more symbols are placed after the symbol of greater value, the values are added

Examples:

• is placed before the symbol of greater value, the symbol of lesser value is XV = 15 (10 + 5 = 15)
• LXXX = 80 (50 + 10 + 10 + 10 = 80)
• MCC = 1200 (1000 + 100 + 100 = 1200)
D. If a symbol subtracted
Examples:
• IV = 4 (5-1 = 4)
• XC = 90 (100- 10) = 90
• CM = 900 (1000- 100 = 900)

Indian System Of Numeration

34, 29, 870 – Thirty four lakh, twenty nine thousand, eight hundred and seventy.

International System Of Numeration

3, 429, 870 – Three million, four hundred and twenty nine thousand eight hundred and seventy.

 Indian System Of Numeration International system of Numeration Lakhs     Thousands     Hundreds     Tens     Ones Hundred Thousands     Thousands     Hundreds     Tens     Ones 41,26,354 126,354 41 Lakhs,26 Thousands,354 Three Hundred and fifty four 126 Hundred Thousands ,354 Three Hundred and fifty four

Difference Between The Indian And International System To Numeration

In both the systems, the first five places remain the same i.e., up to ten thousand.

The rules for writing the number names in the international system of numeration are the same as those for the Indian system of numeration except the difference of places and periods.

Example:
Write the number name of 3429870 in both the systems

Hindu-Arabic numbers

They are given in the table below with their values in Hindu-Arabic numerals.

Predecessor:
A number that comes just before a given number is called a Predecessor.
To find the predecessor of a given number, we subtract 1 from the number.

Examples:

1. The predecessor of the number 43, 21, 679 is 43, 21, 678.
2. The predecessor of the number 2, 24, 00, 000 is 2, 23, 99, 999.

Successor:
A number that comes just after the given number is called its Successor.
To find the successor of a number, we add 1 to the given number.
Examples:

1. The successor of 79, 34, 12, 615 is 79, 34, 12, 616.
2. The successor of 6, 24, 42, 829 is 6, 24, 42, 830.

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