Numbers
In class IV, we have learnt up to 6-digit numbers.
The largest 6-digit number is 9,99,999 and is read as nine lakh ninety-nine thousand nine hundred ninety-nine.
What is 9,99,999 + 1?
When we add 1 to 9,99,999 we get 10,00000 and is read as 10 lakh.
- Indian Place Value Chart
- Place Value and Face Value of a Digit
- Expanded Form
- Comparison of Numbers
- Successor and Predecessor of a Number
- Building the Smallest and the Greatest Numbers
- International Place Value System
- Rounding off Numbers
- Roman Numerals
99,99,999 (Ninety-nine lakh ninety-nine thousand nine hundred ninety-nine) is the largest 7-digit number.
9,99,99,999 (Nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-nine) is the largest 8-digit number.
99,99,99,999 (Ninety-nine crore ninety-nine lakh ninety-nine thousand nine hundred ninety-nine) is the largest 9-digit number.
Indian Place Value Chart
Here is the place value chart upto 10 crore.
| 1 | Ones |
| 10 | Tens |
| 100 | Hundreds |
| 1000 | Thousands |
| 10,000 | Ten Thousands |
| 1,00000 | Lakhs |
| 10,00000 | Ten Lakhs |
| 1,0000000 | Crore |
| 10,0000000 | Ten Crore |
In the above chart, the places are grouped into four periods.The first three places are under the ones period, the next two places are under the thousands period, the next two places are under the lakhs period and the last two places are under the crores period
To read large numbers, we use these periods.
| Number | Number Name |
|---|---|
| 2,90,534 | Two Lakh Ninety Thousand Five Hundred thirty-four |
| 4,59,861 | Four lakh Fifty-nine Thousand Eight Hundred Sixty-one |
| 3,42,25,941 | Three crore forty-two lakh twenty-five Thousand Nine Hundred Forty-one |
| 16,89,75,245 | Sixteen crore Eighty-nine Lakh Seventy-five Thousand Two Hundred Forty-five |
3,42,25,941
Three crore forty-two lakh twenty-five Thousand Nine Hundred Forty-one
Three crores forty-two lakhs twenty-five Thousands Nine Hundred Forty-one
Three crore forty-two lakh twenty-five Thousand Nine Hundred and Forty-one
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.
| Crores | Lakhs | Thousands | Ones | |||||
| 1 | 2 | 6 | 8 | 4 | 2 | 3 | 2 | 5 |
| Crores | Lakhs | Thousands | Ones | |||||
| 1 | 2 | 6 | 8 | 4 | 2 | 3 | 2 | 5 |
| 12,0000000 | 68,00000 | 42,000 | 300 | 20 | 5 | |||
Comparison of Numbers
In this case, the number with more digits is greater than the other.
2055426 is greater than 250256 as 2055426 is a 7-digit number and 250256 is a 6-digit number
2055426 > 250256
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 | ||
|---|---|---|
| 250586 | 205486 | 250486 > 205486 |
| 1001 | 1010 | 1001 < 1010 |
| 2050156 | 250256 | 2050156 > 250256 |
| 452585125 | 452585152 | 452585125 < 452585152 |
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 |
|---|---|---|
| 1000000 | 1000001 | 999999 |
| 50000 | 50001 | 49999 |
| 2508 | 2509 | 2507 |
| 25000 | 25001 | 24999 |
Building the Smallest and the Greatest Numbers
Consider the numbers 3, 4, 2, 0, 7, 9 and 5.
Using these digits only once, let us form the smallest and the greatest 7-digit numbers.
To get the greatest 7-digit number, we will arrange the digits in descending order and to get the smallest 7-digit number, we will arrange the digits in ascending order.
Hence, 2034579 is the smallest and 9754320 is the greatest.
International Place Value System
many countries use the International place-value system which is slightly different from the Indian numbering system.
Here is the International place-value chart for the first 6 places.
| 1 | Ones |
| 10 | Tens |
| 100 | Hundreds |
| 1000 | Thousands |
| 10,000 | Ten Thousands |
| 100,000 | Hundred Thousands |
In the above chart, the places are grouped into two periods.The first three places are under the ones period and the next three places are under the thousands period.
| Number | Number Name in the International system |
|---|---|
| 38,946 | Thirty-eight Thousand Nine Hundred Forty-six |
| 290,534 | Two Hundred Ninety Thousand Five Hundred thirty Four |
| 400,861 | Four Hundred Thousand Eight Hundred Sixty-one |
Rounding off Numbers
In some accassions, we require only a rough estimation and not the exact value. In such cases, we round off the values to the nearest tens or hundreds or thousands.
1. Identify the nearest ten or hundred or thousand of the number (both above and below).
2. When the number is exactly in the middle, always round up to the nearest ten or hundred or thousand.
3. When the number is below the mid number, always round down to the nearest ten or hundred or thousand.
4. When the number is above the mid number, always round up to the nearest ten or hundred or thousand
| Number | Rounds to | Action |
|---|---|---|
| 155 | 160 | Rounded up to the nearest ten. |
| 155 | 200 | Rounded up to the nearest hundred. |
| 2544 | 2540 | Rounded down to the nearest ten. |
| 2544 | 2500 | Rounded down to the nearest hundred. |
| 2544 | 3000 | Rounded up to the nearest thousand. |
Roman Numerals
In class IV, we learnt how to write numbers up to 40 using Roman Numerals. Here we will learn Roman Numerals upto 100.
The Roman Numeration System uses only 7 symbols to write any number.
They are I, V, X, L, C, D and M,br>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
| Numbers with Roman representation | |||
|---|---|---|---|
| 1 | I | 51 | LI |
| 2 | II | 52 | LII |
| 3 | III | 53 | LIII |
| 4 | IV | 54 | LIV |
| 5 | V | 55 | LV |
| 6 | VI | 56 | LVI |
| 7 | VII | 57 | LVII |
| 8 | VIII | 58 | LVIII |
| 9 | IX | 59 | LIX |
| 10 | X | 60 | LX |
| 11 | XI | 61 | LXI |
| 12 | XII | 62 | LXII |
| 13 | XIII | 63 | LXIII |
| 14 | XIV | 64 | LXIV |
| 15 | XV | 65 | LXV |
| 16 | XVI | 66 | LXVI |
| 17 | XVII | 67 | LXVII |
| 18 | XVIII | 68 | LXVIII |
| 19 | XIX | 69 | LXIX |
| 20 | XX | 70 | LXX |
| 21 | XXI | 71 | LXXI |
| 22 | XXII | 72 | LXXII |
| 23 | XXIII | 73 | LXXIII |
| 24 | XXIV | 74 | LXXIV |
| 25 | XXV | 75 | LXXV |
| 26 | XXVI | 76 | LXXVI |
| 27 | XXVII | 77 | LXXVII |
| 28 | XXVIII | 78 | LXXVIII |
| 29 | XXVIX | 79 | LXXIX |
| 30 | XXX | 80 | LXXX |
| 31 | XXXI | 81 | LXXXI |
| 32 | XXXII | 82 | LXXXII |
| 33 | XXXIII | 83 | LXXXIII |
| 34 | XXXIV | 84 | LXXXIV |
| 35 | XXXV | 85 | LXXXV |
| 36 | XXXVI | 86 | LXXXVI |
| 37 | XXXVII | 87 | LXXXVII |
| 38 | XXXVIII | 88 | LXXXVIII |
| 39 | XXXIX | 89 | LXXXIX |
| 41 | XLI | 90 | XC |
| 42 | XLII | 91 | XCI |
| 43 | XLIII | 92 | XCII |
| 44 | XXXIII | 93 | XCIII |
| 34 | XLIV | 94 | XCIV |
| 45 | XLV | 95 | XCV |
| 46 | XLVI | 96 | XCVI |
| 47 | XLVII | 97 | XCVII |
| 48 | XLVIII | 98 | XCVIII |
| 49 | XLIX | 99 | XCIX |
| 50 | L | 100 | C |