Subject: Compulsory Maths

It is the number system in which ten digits (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 ,9 ) are used. Any whole number can be written using a combination of these ten digits. As it is based on the grouping of tens, it is also known as Decimal Number System or the Base Ten System. The value of each digit in a number depends on its place in the number. For example:

6 9 8 2

Thus, we can obtain the place value of any digit in a number by multiplying the digit by its place. So,the above number can also be expressed in expanded form as:

6982 = 6× 1000 + 9× 100 + 8× 10 + 2× 1

= 6× 10^{3} + 9× 10^{2} + 8× 10^{1} + 2× 10^{0} [\(\because\) 10^{0 }= 1]

**Nepali System**The table below shows the periods and places of number in Nepali system:

Periods | Kharabs | Arabs | Crores | Lakhs | Thousands | Units | |||||||

Places | Ten Kharabs | Kharabs | Ten Arabs | Arabs | Ten Crores | Crores | Ten Lakhs | Lakhs | Ten Thousand | Thousand | Hundred | Tens | Once |

Power of 10 | 10^{1}^{2} | 10^{11} | 10^{10} | 10^{9} | 10^{8} | 10^{7} | 10^{6} | 10^{5} | 10^{4} | 10^{3} | 10^{2} | 10^{1} | 10^{0} |

Number | 6 | 9 | 2 | 4 | 3 | 1 | 7 | 2 | 8 | 0 | 1 | 6 |

From the above table, the number name of 692431728016 is:

Six kharab ninety-two arab forty-three crores seventeen lakh twenty-eight thousand sixteen.

**International System**

Periods | Bllions | Millions | Thousands | Units | ||||||||

Places | Hundred Billions | Ten Billions | Billions | Hundred Millions | Ten Millions | Millions | Hundred Thousands | Ten Thousand | Thousands | Hundreds | Tens | Once |

Power of 10 | 10^{11} | 10^{10} | 10^{9} | 10^{8} | 10^{7} | 10^{6} | 10^{5} | 10^{4} | 10^{3} | 10^{2} | 10^{1} | 10^{0} |

Number | 6 | 9 | 2 | 4 | 3 | 1 | 7 | 2 | 8 | 0 | 1 | 6 |

In International system, the number name of 692431728016:

Six hundred ninety-two billion four hundred thirty-one million seven hundred twenty-eight thousand sixteen.

**Use of commas in Nepali system**

At first, units period is separated, then the numbers of places of thousand, lakhs, crores etc are separated. For examples, 692431728016 is written as Six kharab ninety-two arab forty-three crores seventeen lakh twenty-eight thousand sixteen.At first, units period is separated, then the numbers of places of thousands, millions and billions are separated. For example,692431728016 is written as Six hundred ninety-two billion four hundred thirty-one million seven hundred twenty-eight thousand sixteen.**Use of commas International system**

- It is the number system in which ten digits (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 ,9 ) are used. Any whole number can be written using a combination of these ten digits. As it is based on the grouping of tens, it is also known as Decimal Number System or the Base Ten System.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

Re-write the numerals using commas according to Nepali as well as an International system. Then write the number name in the both systems.

485913082

Solution:

In Nepali System,

48,59,13,082 = Forty-eight crores fifty-nine lakhs thirteen thousands and eighty-two.

In International System,

485,913,082 = Four hundred eighty-five million nine hundred thirteen thousand and eighty-two.

The distance between the sun and the earth is about fifteen crore twenty lakh kilometer. Write this distance in numeral using commas according to Nepali and International systems. Re-write the number name in International system.

Solution:

In Nepali system,

fifteen crores twenty lakh kilometer = 15,20,00,000

In International system,

fifteen crore twenty lakh kilometer = 152, 000, 000

One hundred fifty two million.

How many lakhs are in one million ?

Solution:

There are 10 lakhs in 1 million

Expand the 268795438 numerals in powers of 10.

Solution;

In Nepali system,

268795438 = 2 × 10^{8} + 6 × 10^{7} + 8 × 10^{6} + 7 × 10^{5} + 9 × 10^{4} + 5 × 10^{3} + 4 × 10^{2} + 3 × 10 ^{1} + 8 × 10^{0}

Re-write 7236095841numerals using commas according to Nepali as well as an International system. Then write the num,ber name in the both system.

Solution:

In Nepali system,

7,23,60,95,841 = Seven arab twenty-three crore sixty lakh ninety-five thousand eight hundred and forty-one.

In International system,

7,236,095,841 = Seven billion two hundred thirty-six million ninety-five thousand eight hundred and forty-one.

Re-write 905730218645 numerals using commas according to Nepali as well as an International system. Then write the num,ber name in the both system.

Solution:

In Nepali system,

9,05,73,02,18,645 = Nine kharab five arab seventy-three crore two lakh eighteen thousand six hundred and forty five.

In International system,

905,730,218,645 = Nine hundred five billion seven hundred thirty million two hundred eighteen thousand six hundred and forty-five.

Expand 800405907623 numerals in a power of 10.

Solution:

8 × 10^{11} + 4 × 10^{8} + 9 × 10^{5 }+ 7 × 10^{3} + 6 × 10^{2} + 2 × 10^{1} + 3 × 10^{0}

How much is ten billion in Nepali system?

Solution:

It is Ten arab of ten billion in Nepali system.

Write the given numerals in short form.

9 × 10^{12} + 6 × 10^{8 }+ 5 × 10^{2}

Solution:

9 × 10^{12} + 6 × 10^{8 }+ 5 × 10^{2 }= 9000600000500

Write the given numerals in short form.

3 × 10^{9} + 5 × 10^{7} + 8 × 10^{4} + 9

Solution:

3 × 10^{9} + 5 × 10^{7} + 8 × 10^{4} + 9 = 3050080009

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