# Class 3 Number System

Introduction of Bigger Numbers

## Class II Recap

Till now, we have learnt numbers up to 999 and the additions and subtraction operations. Let us review the reading and writing of numbers up to 999.

**Example 1.**Write the number names for the following numbers.

i) 74 ii) 645 iii) 942

**Solution.**

i) 74 = Seventy Four

ii) 645 = Six hundred forty five

iii) 942 = Nine hundred forty two

**Example 2.**Write the following numbers.

i) Sixty seven

ii) Four hundred thirty five

iii) Eight hundred sixty

**Solution.**

i) Sixty seven = 67

ii) Four hundred thirty five = 435

iii) Eight hundred sixty = 860

**Example 3.**Write the numbers

i) 4 hundreds 4 tens 3 ones

ii) 9 tens 9 ones

iii) 9 hundred 5 ones

**Solution.**

i) 4 hundreds 4 tens 3 ones = 443

ii) 9 tens 9 ones = 99

iii) 9 hundred 5 ones = 905

## Introduction of Bigger Numbers

What we shall get when 1 is added to 999?

999 + 1 = 9 hundreds + 9 tens + 9 ones + 1 ones

= 9 hundreds + 9 tens + 1 tens ----> (9 ones + 1 ones = 10 ones = 1 tens)

= 9 hundreds + 10 tens ----> (9 tens + 1 tens = 10 tens = 1 hundreds)

= 9 hundreds + 1 hundreds

= 10 hundreds = 1 thousand = 1000

*1000 is the smallest number of four digits*

*10 hundreds = 1 thousand *

*We read 1000 as One thousand*

1001 = 1 thousands, 0 hundreds, 0 tens and 1 ones. It is read as one thousand one.

1005 = 1 thousands, 0 hundreds, 0 tens and 5 ones. It is read as one thousand five.

1010 = 1 thousands, 0 hundreds, 1 tens and 0 ones. It is read as one thousand ten.

1100 = 1 thousands, 1 hundreds, 0 tens and 0 ones. It is read as one thousand one hundred.

1200 = 1 thousands, 2 hundreds, 0 tens and 0 ones. It is read as one thousand two hundred.

2000 = 2 thousands, 0 hundreds, 0 tens and 0 ones. It is read as two thousand.

2001 = 2 thousands, 0 hundreds, 0 tens and 1 ones. It is read as two thousand one.

2005 = 2 thousands, 0 hundreds, 0 tens and 5 ones. It is read as two thousand five.

2010 = 2 thousands, 0 hundreds, 1 tens and 0 ones. It is read as two thousand ten.

2100 = 2 thousands, 1 hundreds, 0 tens and 0 ones. It is read as two thousand one hundred.

2200 = 2 thousands, 2 hundreds, 0 tens and 0 ones. It is read as two thousand two hundred.

3000 is read as three thousand, 4000 is read as four thousand , 5000 is read as five thousand.

6000 is read as six thousand, 7000 is read as seven thousand, 8000 is read as eight thousand.

9000 is read as nine thousand.

9999 is read as nine thousand nine hundred ninety nine.

*9999 is the greatest number of four digits.*

What number we shall get by adding 1 to 9999.

9999 + 1 = 9 thousands + 9 hundreds + 9 tens + 9 ones + 1 ones

= 9 thousands + 9 hundreds + 9 tens + 1 tens

= 9 thousands + 9 hundreds + 10 tens (10 tens = 1 hundred)

= 9 thousands + 9 hundreds + 1 hundred

= 9 thousands + 10 hundreds (10 hundreds = 1 thousand)

= 9 thousands + 1 thousand

= 10 thousands = 10000

We read 10000 as ten thousand, 10000 is the smallest number of five digits.

10001 = 1 ten thousands 0 thousands 0 hundreds 0 tens and 1 ones. It is read as ten thousand one.

10005 = 1 ten thousands 0 thousands 0 hundreds 0 tens and 5 ones. It is read as ten thousand five.

10010 = 1 ten thousands 0 thousands 0 hundreds 1 tens and 0 ones. It is read as ten thousand ten.

10100 = 1 ten thousands 0 thousands 1 hundreds 0 tens and 0 ones. It is read as ten thousand one hundred.

10105 = 1 ten thousands 0 thousands 1 hundreds 0 tens and 5 ones. It is read as ten thousand one hundred five.

10150 = 1 ten thousands 0 thousands 1 hundreds 5 tens and 0 ones. It is read as ten thousand one hundred fifty.

10200 = 1 ten thousands 0 thousands 2 hundreds 0 tens and 0 ones. It is read as ten thousand two hundred.

10300 = 1 ten thousands 0 thousands 3 hundreds 0 tens and 0 ones. It is read as ten thousand three hundred.

10400 = 1 ten thousands 0 thousands 4 hundreds 0 tens and 0 ones. It is read as ten thousand four hundred.

10500 = 1 ten thousands 0 thousands 5 hundreds 0 tens and 0 ones. It is read as ten thousand five hundred.

10600 = 1 ten thousands 0 thousands 6 hundreds 0 tens and 0 ones. It is read as ten thousand six hundred.

10700 = 1 ten thousands 0 thousands 7 hundreds 0 tens and 0 ones. It is read as ten thousand seven hundred.

10800 = 1 ten thousands 0 thousands 8 hundreds 0 tens and 0 ones. It is read as ten thousand eight hundred.

10900 = 1 ten thousands 0 thousands 9 hundreds 0 tens and 0 ones. It is read as ten thousand nine hundred.

11000 = 1 ten thousands 1 thousands 0 hundreds 0 tens and 0 ones. It is read as eleven thousand.

30000 = 3 ten thousands 0 thousands 0 hundreds 0 tens and 0 ones. It is read as thirty thousand.

50000 = 5 ten thousands 0 thousands 0 hundreds 0 tens and 0 ones. It is read as fifty thousand.

80000 = 8 ten thousands 0 thousands 0 hundreds 0 tens and 0 ones. It is read as eighty thousand.

90000 = 9 ten thousands 0 thousands 0 hundreds 0 tens and 0 ones. It is read as ninety thousand.

99999 = 9 ten thousands 9 thousands 9 hundreds 9 tens and 9 ones. It is read as ninety nine thousand nine hundred ninety nine.

## Number Names

Ten-thousands | Thousands | Hundreds | Tens | Ones |
---|---|---|---|---|

5 | 8 | 9 | 2 | |

8 | 6 | 0 | 7 | 6 |

9 | 2 | 3 | 6 | 4 |

In the above table, 1st number is written as 5 thousands 8 hundreds 9 tens 2 ones, that is 5892.
We write as five thousand eight hundred ninety two.

2nd number is written as 8 ten thousands 6 thousands 0 hundreds 7 tens 6 ones, that is 86076.
We write as eighty six thousand seventy six.

3rd number is written as 9 ten thousands 2 thousands 3 hundreds 6 tens 4 ones, that is 92364.
We write as ninety two thousand three hundred sixty four.

1 tens = 10 ones

1 hundred = 10 tens = 100 ones

1 thousands = 10 hundreds = 100 tens = 1000 ones

1 ten thousands = 10 thousands = 100 hundreds = 1000 tens = 10000 ones

## Exapanded Forms of Numbers

A number is consists of thousands , hundreds , tens and ones. For example, 9546 number has
9 thousands 5 hundreds 4 tens and 6 ones.

That means 9546 = 9000 + 500 + 40 + 6

Similarly 84567 has 8 Ten-thousands 4 thousands 5 hundreds 6 tens and 7 ones

84567 = 80000 + 4000 + 500 + 60 + 7

Writing of numbers in short form from expanded form.

4000 + 700 + 60 + 9 = 4 thousands 7 hundreds 6 tens and 9 ones

= 4000 + 700 + 60 + 9 = 4769

70000 + 6000 + 300 + 90 + 1 = 7 ten-thousands 6 thousands 3 hundreds 9 tens 1 ones

= 70000 + 6000 + 300 + 90 + 1 = 76391

50000 + 600 + 50 + 5 = 5 ten thousands 0 thousands 6 hundreds 5 tens 5 ones

= 50000 + 600 + 50 + 5 = 50655

## Place Value

Place Value is nothing but Ten-thousands, thousands, hundreds , tens and ones. For example, place value of 5 in number 25637 is 5 thousand.

Face value are nothing but the digits of the numbers, i.e. 1, 2, 3, 4, 5, 6, 7, 8 & 9. For example, face value of 3 in the numbers 312, 4534, 43565 is 3.

Place value of a digit changes according to the place it occupies in the number. But, the face value remain unchanged and is the value of the digit itself.

Place value table and some examples

Number | Ten-thousands | Thousands | Hundreds | Tens | Ones |
---|---|---|---|---|---|

567 | 5 | 6 | 7 | ||

5246 | 5 | 2 | 4 | 6 | |

26587 | 2 | 6 | 5 | 8 | 7 |

**Example 1.**Find the place value of each digit in 1975.

**Solution.**

We can know the place value of a digit using expanded form of a number.

**Example 2.**Find the place value of 6 in 9645.

**Solution.**Expanded form of 9645 is

9645 = 9000 + 600 + 40 + 4

So place value of 6 is 600.

## Relation Between Numbers

We have already known the method of getting the greater number between two 3 digits numbers. Here we shall learn the method of knowing the greater number between two given 4 digits or 5 digits numbers.

** Rule no. 1** The number which is having more digits is greater than the number having a smaller number of digits.

**Example.** 27 > 9, 456 > 99, 8745 > 987

** Rule No. 2** If the two numbers have the same number of digits then we compare the extreme left
digits and decide which is larger. If the extreme left digits of the two numbers are same, we keep
on comparing the next digits on the right.

**Example.** 567 > 230, 5894 > 5678, 85678 > 85572

## Ascending-Descending Order

Ascending Order : Arranging numbers from Smaller to Greater.

Descending Order :- Arranging numbers from greater to smaller.

**Example 1.** Write the following numbers in ascending order

7535, 8538, 8987, 675, 45

**Solution.** Smallest number is 45, the next number which is greater than 45 is 675.
The other numbers greater than 675 in order are 7535, 8538 and 8987.

All the given numbers written in ascending order are : 45, 675, 7535, 8538, 8987.

**Example 2.** Write the following numbers in descending order

565, 38345, 48001, 48035, 12265, 8440

**Solution.** In the above numbers greatest number is 48035. The next number smaller than 48035 is 48001.
The other number smaller than 48001 in order are 38345, 12265, 8440, 565.

All the given numbers when written in descending order are:48035, 48001, 38345,12265, 8440, 565

## Successor-Predecessor

**Successor:** Number that comes just after a particular number is called it s successor.

Number | Method | Successor |
---|---|---|

285 | 285+1 | 286 |

5039 | 5039+1 | 5040 |

49885 | 49885+1 | 49886 |

**Predecessor:** Number that comes just before a particular number is called it s predecessor.

Number | Method | Predecessor |
---|---|---|

285 | 285-1 | 284 |

5039 | 5039-1 | 5038 |

49885 | 49885-1 | 49884 |

We can get the Predecessor of a number by subtracting 1 from the given number.

## Smallest and Greatest Numbers

** Smallest Number** formation: For example, let s consider 4 digits number and integers that we will use
are 5, 7, 9 and 1. Using these integers we have to form smallest number, first we select the smallest
integer and write it in the thousands place, then we write the next greater integer in the hundred s place,
then we write the next greater integer in the ten s place and lastly the greatest integer in the one s place.

Smallest number is 1579

Thousand s Place | Hundred s Place | Ten s Place | One s Place |
---|---|---|---|

1 | 5 | 7 | 9 |

** Greatest Number formation:** If we want to form the greatest number of 4 digits, using all the given
integers (3,6,8,9) without repetition. First we have to select the greatest integer (9) and write it in the thousand s
place, then we have to write the next smaller integer (8) in the hundred s place. Next we have to write smaller integer (6)
in ten s place and at last write the smallest integer in the one s place.

Greatest number is 9863.

Thousand s Place | Hundred s Place | Ten s Place | One s Place |
---|---|---|---|

9 | 8 | 6 | 3 |

## Class-3 Number System Test

## Class-3 Number System Worksheet

## Answer Sheet

**Number-System-Answer**Download the pdf

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