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References

**Natural numbers**

Counting numbers 1, 2, 3, 4, ...... etc. are called Natural numbers. The smallest natural number is 1 and there is no largest natural number.

**Digits**

Numbers are formed using the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These symbols are called digits or figures.

To find the place value of a digit in a number, multiply the digit with the value of the place it occupies.

**Comparison of numbers**

If two numbers have an unequal number of digits, then the number with the greater number of digits is greater. If two numbers have equal number of digits then, the number with greater valued digit on the extreme left is greater. If the digits on extreme left of the numbers are equal then the digits to the right of the extreme left digits are compared and so on.

The greatest single-digit number is 9. When 1 is added to the greatest single-digit number, we get 10, which is the smallest two-digit number. Therefore, the greatest single-digit number + 1 = the smallest two-digit number.

The greatest two digit-number is 99. When 1 is added to the greatest two-digit number, we get 100, which is the smallest three-digit number. Therefore, the greatest two-digit number + 1 = the smallest three-digit number.

The greatest three-digit number is 999. When 1 is added to the greatest three-digit number, we get 1000, which is the smallest four-digit number. Therefore, the greatest three-digit number + 1 = the smallest four-digit number.

The greatest four-digit number is 9999. When 1 is added to the greatest four-digit number, we get 10,000, which is the smallest five-digit number. Therefore, the greatest four-digit number + 1 = the smallest five-digit number.

The greatest five-digit number is 99999. When 1 is added to the greatest five-digit number, we get 1,00,000, which is the smallest six digit number. Therefore, the greatest five-digit number + 1 = the smallest six-digit number. The number, that is, one with five zeroes (100000), is called one lakh.

The greatest six-digit number is 999999. When 1 is added to the greatest six-digit number, we get 10,00,000, which is the smallest seven-digit number. Therefore, the greatest six-digit number + 1 = the smallest seven-digit number. The number, that is, one with six zeroes (1000000), is called ten lakh.

The greatest seven-digit number is 9999999. When we add 1 to this seven-digit number, we get 10000000, which is the smallest eight-digit number. Therefore, the greatest seven-digit number + 1 = the smallest eight-digit number. The number, that is, one with seven zeroes (10000000),is called one crore.

**Indian system of numeration**

Values of the places in the Indian system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousands, Lakhs, Ten Lakhs, Crores and so on.

The following place value chart can be used to identify the digit in any place in the Indian system.

Periods |
Crores | lakhs | Thousands | Ones | |||||

Places |
Tens | Ones | Tens | Ones | Tens | Ones | Hundreds | Tens | Ones |

**International system of numeration**

Values of the places in the International system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousands, Hundred thousands, Millions, Ten millions and so on.

1 million = 1000 thousands,

1 billion = 1000 millions

Following place value chart can be used to identify the digit in any place in the International system.

Periods |
Billions | Millions | Thousands | Ones | ||||||||

Places |
Hundreds | Tens | Ones | Hundreds | Tens | Ones | Hundreds | Tens | Ones | Hundreds | Tens | Ones |

**Comparison of the Indian and the international numeration systems**

Indian Numeration |
Crore | Ten Lakh | Lakh | Ten Thousand | Thousand | Hundred | Ten | One |

Numbers |
10000000 | 1000000 | 100000 | 10000 | 1000 | 100 | 10 | 0 |

International Numeration |
Ten Million | Million | Hundred Thousand | Ten Thousand | Thousand | Hundred | Ten | Ones |

**Commas in Indian system of numeration**

Commas are placed to the numbers to help us read and write large numbers easily. As per Indian system of numeration, the first comma is placed after the hundreds place. Commas are then placed after every two digits.

e.g. (i) 88,76,547

The number can be read as eighty-eight lakh seventy-six thousand five hundred and forty-seven.

(ii) 5,67,89,056

The number can be read as five crore sixty-seven lakh eighty-nine thousand and fifty-six.

**Commas in International system of Numeration**

As per International numeration system, the first comma is placed after the hundreds place. Commas are then placed after every three digits.

e.g. (i) 8,876,547

The number can be read as eight million eight hundred seventy-six thousand five hundred and forty-seven.

(ii) 56,789,056

The number can be read as fifty-six million seven hundred eighty-nine thousand and fifty-six.

**Ascending order**

The arrangement of numbers from the smallest to the greatest is called ascending order.

e.g. 2789, 3560, 4567, 7662, 7665

**Descending order**

The arrangement of numbers from the greatest to the smallest is called descending order.

e.g. 7665, 7662, 4567, 3560, 2789

**Formation of numbers**

Numbers can be formed using the given digits with or without repetition of digits.

**Conversion of units of measurement
Units of length**:

1 metre = 100 centimetres

1 centimetre = 10 millimetres

1 kilogram = 1,000 grams

1 gram = 1000 milligrams

1 kilolitre = 1000 litres

1 litre = 1,000 millilitres

**Natural numbers**

Counting numbers 1, 2, 3, 4, ...... etc. are called Natural numbers. The smallest natural number is 1 and there is no largest natural number.

**Digits**

Numbers are formed using the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These symbols are called digits or figures.

To find the place value of a digit in a number, multiply the digit with the value of the place it occupies.

**Comparison of numbers**

If two numbers have an unequal number of digits, then the number with the greater number of digits is greater. If two numbers have equal number of digits then, the number with greater valued digit on the extreme left is greater. If the digits on extreme left of the numbers are equal then the digits to the right of the extreme left digits are compared and so on.

The greatest single-digit number is 9. When 1 is added to the greatest single-digit number, we get 10, which is the smallest two-digit number. Therefore, the greatest single-digit number + 1 = the smallest two-digit number.

The greatest two digit-number is 99. When 1 is added to the greatest two-digit number, we get 100, which is the smallest three-digit number. Therefore, the greatest two-digit number + 1 = the smallest three-digit number.

The greatest three-digit number is 999. When 1 is added to the greatest three-digit number, we get 1000, which is the smallest four-digit number. Therefore, the greatest three-digit number + 1 = the smallest four-digit number.

The greatest four-digit number is 9999. When 1 is added to the greatest four-digit number, we get 10,000, which is the smallest five-digit number. Therefore, the greatest four-digit number + 1 = the smallest five-digit number.

The greatest five-digit number is 99999. When 1 is added to the greatest five-digit number, we get 1,00,000, which is the smallest six digit number. Therefore, the greatest five-digit number + 1 = the smallest six-digit number. The number, that is, one with five zeroes (100000), is called one lakh.

The greatest six-digit number is 999999. When 1 is added to the greatest six-digit number, we get 10,00,000, which is the smallest seven-digit number. Therefore, the greatest six-digit number + 1 = the smallest seven-digit number. The number, that is, one with six zeroes (1000000), is called ten lakh.

The greatest seven-digit number is 9999999. When we add 1 to this seven-digit number, we get 10000000, which is the smallest eight-digit number. Therefore, the greatest seven-digit number + 1 = the smallest eight-digit number. The number, that is, one with seven zeroes (10000000),is called one crore.

**Indian system of numeration**

Values of the places in the Indian system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousands, Lakhs, Ten Lakhs, Crores and so on.

The following place value chart can be used to identify the digit in any place in the Indian system.

Periods |
Crores | lakhs | Thousands | Ones | |||||

Places |
Tens | Ones | Tens | Ones | Tens | Ones | Hundreds | Tens | Ones |

**International system of numeration**

Values of the places in the International system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousands, Hundred thousands, Millions, Ten millions and so on.

1 million = 1000 thousands,

1 billion = 1000 millions

Following place value chart can be used to identify the digit in any place in the International system.

Periods |
Billions | Millions | Thousands | Ones | ||||||||

Places |
Hundreds | Tens | Ones | Hundreds | Tens | Ones | Hundreds | Tens | Ones | Hundreds | Tens | Ones |

**Comparison of the Indian and the international numeration systems**

Indian Numeration |
Crore | Ten Lakh | Lakh | Ten Thousand | Thousand | Hundred | Ten | One |

Numbers |
10000000 | 1000000 | 100000 | 10000 | 1000 | 100 | 10 | 0 |

International Numeration |
Ten Million | Million | Hundred Thousand | Ten Thousand | Thousand | Hundred | Ten | Ones |

**Commas in Indian system of numeration**

Commas are placed to the numbers to help us read and write large numbers easily. As per Indian system of numeration, the first comma is placed after the hundreds place. Commas are then placed after every two digits.

e.g. (i) 88,76,547

The number can be read as eighty-eight lakh seventy-six thousand five hundred and forty-seven.

(ii) 5,67,89,056

The number can be read as five crore sixty-seven lakh eighty-nine thousand and fifty-six.

**Commas in International system of Numeration**

As per International numeration system, the first comma is placed after the hundreds place. Commas are then placed after every three digits.

e.g. (i) 8,876,547

The number can be read as eight million eight hundred seventy-six thousand five hundred and forty-seven.

(ii) 56,789,056

The number can be read as fifty-six million seven hundred eighty-nine thousand and fifty-six.

**Ascending order**

The arrangement of numbers from the smallest to the greatest is called ascending order.

e.g. 2789, 3560, 4567, 7662, 7665

**Descending order**

The arrangement of numbers from the greatest to the smallest is called descending order.

e.g. 7665, 7662, 4567, 3560, 2789

**Formation of numbers**

Numbers can be formed using the given digits with or without repetition of digits.

**Conversion of units of measurement
Units of length**:

1 metre = 100 centimetres

1 centimetre = 10 millimetres

1 kilogram = 1,000 grams

1 gram = 1000 milligrams

1 kilolitre = 1000 litres

1 litre = 1,000 millilitres