## Arithmetic Chapter 2 Concept Of Seven And Eight Digit Numbers

**Arithmetic Chapter 2 Seven And Eight Digit Numbers**

1. You have already learned that there are ten digits namely : 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

2. Among these 10 digits, taking any seven or eight digits perfect numbers can be formed.

3. These numbers are called seven or eight-digit numbers.

4. For example, taking seven digits such as 0, 1, 2, 3, 4, 5, 6 a perfect number is formed which is 2041365.

5. This number is a seven-digit number.

6. It is to be noted that, with these seven digits actually

7 x 6 x 5 x 4 x 3 x 2 x 1 – 6 x 5 x 4 x 3 x 2 x 1

= 5040 – 720

= 4320

numbers can be formed (using one digit once in each number only).

7. Similarly taking eight digits such as 0, 1, 2, 3, 4, 5, 6, and 7 a perfect number 40326751 is formed.

8. This number is an eight-digit number.

9. Here actually (using one digit once in each number only)

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 – 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40320 – 5040

= 35280 numbers can be formed.

10. So you can form seven and eight-digit perfect numbers by taking any seven and eight digits from ten digits.

## Arithmetic Chapter 2 Value Or Principal Value Or Absolute Value Of A Digit

1. The actual value of a digit in a number is the own value of the digit, which is always the same.

2. The actual value or principal value of a digit is the absolute value of the digit. For example, let us consider the number 25032189.

3. In this number (from left),

- The principal value of 2 is 2
- The principal value of 5 is 5
- The principal value of 0 is 0
- The principal value of 3 is 3
- The principal value of 2 is 2
- The principal value of 1 is 1
- The principal value of 8 is 8
- The principal value of 9 is 9.

4. So in any number, the actual value of 2 is always 2; the actual value of 4 is 4; the actual value of 5 is 5, etc.

5. Anywhere a digit in a number is placed, the actual value of the digit is always the same.

## Arithmetic Chapter 2 The Place Value Of A Digit

1. You know that, in a number, the digit in the extreme right is called the unit’s place digit; the digit next to its left place is called the ten’s place digit.

2. The digit next to its left place is called the hundred’s place digit, …… etc.

3. Thus the list of the places of the

**Digits are arranged from extreme right to left as:**

**In short, they can be written as:**

4. According to this rule, if we proceed towards left then the place value of any place will be multiplied by 10 and if we proceed towards right then the place value of any place will be divided by 10.

5. For example, if we proceed from the lac place towards the left which is in the ten lac place, then the place value will be multiplied by 10.

6. Again if we proceed from the lac place towards the right that is in the ten thousand places, then the place value will be divided by 10.

7. In this way we get,

- The value in the Unit place = 1
- The value in the Ten place = 1 x 10 = 10
- The value in the Hundred place = 1 x 100 or 10 x 10 = 100
- The value in the Thousand place = 100 x 10 = 1000 ,
- The value in the Ten Thousand place = 1000 x 10 = 10000
- The value in the Lac place = 10000 x 10 = 100000
- The value in the Ten Lac place = 100000 x 10 = 1000000
- The value in the Crore place = 1000000 x 10 = 10000000.

8. So the place value of any digit in a number is the product of the actual value of the digit and the place value of the digit where it lies.

9. Let us consider the number 1583246.

10. We want to determine the place value of 8. Then the actual value of 8 = 8.

11. 8 is placed in ten thousand places and the place value of ten thousand is 10000.

12. The place value of the digit 8 = 8 x 10000 = 80000

13. Similarly, the actual value of 2 is 2 and the digit 2 is placed in the hundred places whose place value = 100.

14. The place value of 2 = 2 x 100 = 200 In this way we can determine the place value of any digit in any number.

## Arithmetic Chapter 2 Expansion of a number according to the place value

1. To expand a given number according to the place value write the place value of each digit (keeping the order of the digits correctly) with a “+” sign between any two.

2. Let us take the example that we have, and expand the number 65432019 according to the place value.

3. Then first write the list of the places of the digits, and next find the place values of the digits as follows.

- Place value of 6 = 6 x 10000000 = 60000000
- Place value of 5 = 5 x 1000000 = 5000000
- Place value of 4 = 4 x 100000 = 400000
- Place value of 3 = 3 x 10000 = 30000
- Place value of 2 = 2 x 1000 = 2000
- Place value of 0 = 0 x 100 = 0
- Place value of 1 = 1 x 10 = 10
- Place value of 9 = 9 x 1 = 9

∴ The expanded form of the number 65432019 is

65432019 = 60000000 + 5000000 + 400000 + 30000 + 2000 + 0 + 10 + 9

= 60000000 + 5000000 + 400000 + 30000 + 2000 + 10 + 9

## Arithmetic Chapter 2 Writing a number given in numeral in words and a number given in words in numeral

**Writing a number in words (the number is given in numerals):**

1. Here first write the digits (given in numerals) in the list of the place values.

2. Then express the place values of the digits in words.

3. We consider the number 7540351 which is to be expressed in words.

4. First, write the digits of the given number according to the list of place values as follows.

5. Now expressing the place values in words, we get, Seven ten lac five lac four ten thousand three hundred five ten one unit.

6. This can be written as Seventy-five lac forty thousand three hundred fifty-one.

7. So the given number when expressed in words we get.

8. Seventy-five lac forty thousand three hundred fifty one.

9. According to the place value, when expressed in words, we get,

10. Seven ten lac five lac four ten thousand three hundred five ten one unit.

**Expressing a number in numerals (when the number is given in words) :**

1. When a number is given in words, we have to express it in numerals, then first the digits in the number can be listed properly according to the list of place values.

2. Here special care is to be taken that if there is no digit mentioned in the place value, it should be written “0” in that place.

3. For example, if the number is given in words say “Six crore Three thousand two”.

4. We have to express this number in numerals.

5. Then at first the digits (written in words in the given number) are listed in the list of place values and we get,

6. Here it is observed that there is no digit (in words) mentioned in ten lac, lac, ten thousand, hundred, and tens places so we write 0 in each of these places in the list of place values.

∴ “Six crore three thousand two” = 60003002