Numbers Beyond 9999
- 5 and 6-Digit Numbers
- Indian Place Value Chart
- Writing Large Numbers in Figures
- Place Value and Face Value of a Digit
- Expanded Form
- Comparison of Numbers
- Successor and Predecessor of a Number
- Building Numbers
- Rounding Numbers
- Roman Numerals
5 and 6-Digit Numbers
In the previous class, we learnt numbers upto 9999. 9999 is the biggest 4-digit number.
Do you know, what is 9999 + 1?
9999 + 1 = 10000 and is read as Ten Thousand
10000 + 1 = 10001 and is read as Ten Thousand one
99999 (Ninety nine thousand nine hundred ninety nine) is the biggest 5-digit number
Do you know, what is 99999 + 1?
99999 + 1 = 100000 and is read as Hundred Thousand (or One Lakh)
100000 + 1 = 100001 and is read as One Lakh one
999999 (Nine Lakh Ninety nine thousand nine hundred ninety nine) is the biggest 6-digit number
Indian Place Value Chart
The Indian numbering system is a little different from the International numbering system and we will learn it at a later point of time. In this section we will learn how to read and write large numbers using the indian place-value chart.
| 1 | Ones |
| 10 | Tens |
| 100 | Hundreds |
| 1000 | Thousands |
| 10000 | Ten Thousands |
| 100000 | Lakhs |
| 1000000 | Ten Lakhs |
In the above chart, the places are grouped into three periods.The first three places are under the ones period, the next two places are under the thousands period and the last two places are under the lakhs period
To read large numbers, we use these periods.
| Number | Number Name |
|---|---|
| 38,946 | Thirty Eight Thousand Nine Hundred Forty Six |
| 2,90,534 | Two Lakh Ninety Thousand Five Hundred thirty Four |
| 4,59,861 | Four lakh Fifty Nine Thousand Eight Hundred Sixty One |
4,59,861
Four lakh Fifty Nine Thousand Eight Hundred Sixty One
Four lakhs Fifty Nine Thousands Eight Hundreds Sixty One
Four lakh Fifty Nine Thousand Eight Hundred and Sixty One
Writing Large Numbers in Figures
We use the above place value chart to write numbers in figures.
Step 1: Arrange the numbers into the three periods, first period is for lakhs, second is for thousands and the third is for ones.
| lakhs | Thousands | Ones | ||||
| 0 | 7 | 0 | 9 | 1 | 4 | 5 |
Seven lakh Nine Thousand One Hundred Forty Five is written as 7,09,145
Place Value and Face Value of a Digit
Expanded Form
In expanded form, a number is written as the sum of the place values of its digits.
| Lakhs | Thousands | Ones | ||||
| 0 | 2 | 3 | 5 | 1 | 2 | 6 |
| lakhs | Thousands | Ones | ||||
| 0 | 2 | 3 | 5 | 1 | 2 | 6 |
| 200000 | 30000 | 5000 | 100 | 20 | 6 | |
Comparison of Numbers
In this case, the number with more digits is greater than the other.
205 is greater than 25 as 205 is a 3-digit number and 25 is a 2-digit number
205 > 25
Case 2: When the two numbers have the same number of digits.
Step 1: Compare the digits at the left most place in both the numbers. The number with greater digit at the left most place is the greater number.
Step 2: If the left most digit in both numbers are same, compare the next immediate digit in both the numbers.
The number with greater digit at this place is the greater number.
If this place also has the same digit for both the numbers, repeat the Steps 1 and 2 until you get the greater number.
| Compare the numbers | ||
|---|---|---|
| 250 | 205 | 250 > 205 |
| 1001 | 1010 | 1001 < 1010 |
| 2050 | 250 | 2050 > 250 |
| 4525 | 4530 | 4525 < 4530 |
Successor and Predecessor of a Number
The number that comes just before a given number is called its Predecessor. To find the Predecessor of a given number, we subtract 1 from the given number.
| Number | Successor | Predecessor |
|---|---|---|
| 99 | 100 | 98 |
| 500 | 501 | 499 |
| 2508 | 2509 | 2507 |
| 1000 | 1001 | 999 |
Building Numbers
Consider the numbers 3, 4 and 5.
Using these digits only once, let us form the smallest and the greatest 3-digit numbers.
To get the greatest 3-digit number, we will arrange the digits in descending order and to get the smallest 3-digit number, we will arrange the digits in ascending order.
Hence, 345 is the smallest and 543 is the greatest.
Consider the numbers 2, 0 and 5.
205 is the smallest and 520 is the greatest.
Rounding Numbers
When we round off a number, we express it approximately, rather than precisely.
(i) Rounding to the nearest 10
To round a number to the nearest 10, we first find those two tens , in between them the number lies.
Round 26 to the nearest 10
We know, 26 lies between 20 and 30 and 26 is 6 away from 20 and only 4 away from 30.
26 is closer to 30 than 20.
So, we can round off 26 to 30.
Round 26 to the nearest 10
We know, 26 lies between 20 and 30 and 26 is 6 away from 20 and only 4 away from 30.
26 is closer to 30 than 20.
So, we can round off 26 to 30.
Round 25 to the nearest 10
We know, 25 is 5 away from 20 and 5 away from 30.
25 is exactly in the middle of 20 and 30. In this case, we will round off to the higher ten.
So, we can round off 25 to 30.
(ii) Rounding to the nearest 100
To round a number to the nearest 100, we first find those hundreds , in between them the number lies.
Round 275 to the nearest 100
We know, 275 lies between 200 and 300 and 275 is closer to 300.
So, we can round up 275 to 300.
Round 440 to the nearest 100
We know, 440 lies between 400 and 500 and 440 is closer to 400.
So, we can round down 440 to 400.
Round 250 to the nearest 100
We know, 250 is exactly in the middle of 200 and 300. In this case, we will round up to the higher hundred.
So, we can round up 250 to 300.
(iii) Rounding to the nearest 1000
To round a number to the nearest 1000, we first find those thousands , in between them the number lies.
Round 4580 to the nearest 1000
We know, 4580 lies between 4000 and 5000 and 4580 is closer to 5000.
So, we can round up 4580 to 5000.
Round 7200 to the nearest 1000
We know, 7200 lies between 7000 and 8000 and 7200 is closer to 7000.
So, we can round down 7200 to 7000.
Round 2500 to the nearest 1000
We know, 2500 is exactly in the middle of 2000 and 3000. In this case, we will round up to the higher thousand.
So, we can round up 2500 to 3000.
Roman Numerals
In the international numbering system, we use 10 symbols (digits) to write any number. They are
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
Unlike the international numbering system, the Roman Numeration System uses only 7 symbols to write any number.
They are I, V, X, L, C, D and M
The values of these symbols are given below:
| Roman Numeral | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
Rule 1: Repetition of a Roman Numeral means addition
Example: III = 1 + 1 + 1 = 3,
XX = 10 + 10 = 20
Rule 2: If a smaller numeral is written to the right of a greater Roman numeral, then the smaller is always added to the greater one.
Example: VII = 5 + 1 + 1 = 7,
XV = 10 + 5 = 15,
XXVI = 10 + 10 + 5 + 1 = 26
Rule 3: If a smaller numeral is written to the left of a greater Roman numeral, then the smaller is always subtracted from the greater one.
Example: IV = 5 - 1 = 4,
IX = 10 - 1 = 9,
XIX = 10 + (10 - 1) = 19
1. There is no zero in the Roman System.
2. There is no concept of place value in the Roman System.
3. No symbol will repeat continuosely more than three times in any number
Example: 9 is written as IX, not as VIIII, 40 is written as XL, not as XXXX
| Number | Roman | Number | Roman |
|---|---|---|---|
| 1 | I | 21 | XXI |
| 2 | II | 22 | XXII |
| 3 | III | 23 | XXIII |
| 4 | IV | 24 | XXIV |
| 5 | V | 25 | XXV |
| 6 | VI | 26 | XXVI |
| 7 | VII | 27 | XXVII |
| 8 | VIII | 28 | XXVIII |
| 9 | IX | 29 | XXVIX |
| 10 | X | 30 | XXX |
| 11 | XI | 31 | XXXI |
| 12 | XII | 32 | XXXII |
| 13 | XIII | 33 | XXXIII |
| 14 | XIV | 34 | XXXIV |
| 15 | XV | 35 | XXXV |
| 16 | XVI | 36 | XXXVI |
| 17 | XVII | 37 | XXXVII |
| 18 | XVIII | 38 | XXXVIII |
| 19 | XIX | 39 | XXXIX |
| 20 | XX | 40 | XL |