6th Class Mathematics Knowing our Numbers Indian Number System or Hindu-Arabic Number System

  Indian Number System or Hindu-Arabic Number System

This system was introduced by Indians therefore, called Indian number system. In this system 10 is considered as the base.

10 units = 10, 10 tens = 1 hundred, 10 hundreds = 1 thousand

Hindu -Arabic number system is based on the place value of the numbers. A single number is read as once and first digit from the right side of more than one digit number is also read as once while second, third, fourth, fifth, digits from right side are read as tens, hundreds, thousands, ten thousands respectively.  

Indian Place Value Chart         

The number ninety eight thousand seven hundred and thirty five is written by placing. 9 at the place of "Ten thousands", 8 at "Thousands", 7 at "Hundreds".3 at "Tens", 5 at "Ones" place, therefore, the expanded from of the number 98735  \[=9\times 10000+8\text{ }\,\,\,1000+7\times 100+3\times 10+5.\] The number twenty five lakhs, seventy eight thousand, sixty hundred and thirty two is written by placing 2 at ten lakhs, 5 at lakhs, 7 at ten thousands, 8 at thousands,   6 at the place of hundreds, 3 at tens, 2 at ones, therefore, the expanded form of the number,                

\[2578632=2\times 1000000+5\times 100000\]\[+7\times 10000+8\times 1000+6\times 100+3\times 10+2.\]

The place value of 5 in the number 65744678 is:

(a) 5 lakhs                                           

(b) 57 lakhs

(c) 50 lakhs                                         

(d) None of these

(e) All of these  

Answer: (c)

Explanation

Place value of 5 in the numerals 65744678 is 50 lakhs.  

Place Value

If a number contains more than one digit then the place occupies by each digit is its place value. In the number 732 the number 7 occupies the place of hundreds, therefore, the place value of 7 in the number is seven hundred. The number 3occupies the place of tens and therefore, the place value of 3 in the number is 30and the number 2 occupies the place of ones therefore, the place value of 2 in the number is 2.                            

Expanded form of number 732 is, \[732=7\times 100+3\times 10+2\times 1.\]

Find the difference of place values of 4 in the number 54675846.

(a) 390099                                          

(b) 3999960

(c) 5400000                                        

(d) All of these

(e) None of these  

Answer: (b)

Explanation

Difference of place values of 4 in the numeral 54675846 = 4000000 - 40 = 3999960.  

Comparison between Indian and International Number System

  In the above table the equivalent of Indian in terms of international number systemhas been given. The place value of digits of number 320075066 are:  

Three hundred five billion six million and four hundred ninety nine is written by which one of the following numbers?

(a) 305006000499                            

(b) 305,600,0499

(c) 305,60,000,4,99                          

(d) All of these

(e) None of these  

Answer: (a)

Explanation

Three hundred five billion six million and four hundred ninety nine = 305,006000499.  

Face Value

The face value of a number does not change regardless of the place it occupies. Therefore, the face value of a number is the number itself. In the number 732 face value of 7 is seven, the face value of 3 is three and the face value of 2 is 1    

Find the difference between the face value of 9 and 5 in any number.

(a) 4                                                      

(b) 13

(c) 45                                                    

(d) All of these

(e) None of these  

Answer: (a)                

Explanation

9 - 5 = 4.                

International Place Value Chart  

The above chart is the international place value chart.

The number 5,684,325,431, in the above chart read as five billion, six hundred eighty four million, three hundred twenty five thousand, four hundred thirty one. The expanded form of the number 5684325431 is:  

5684325431 = 5000000000 + 600000000 + 80000000 + 4000000 + 300000 + 20000+ 5000 +400+30+1      

Which one of the following options represents the numerals 6403955025 in words in Indian and international number system?

(a) Indian system: Six Kharab forty crore thirty nine lakh fifty five thousand and twenty five. International system: Six million four hundred three million nine hundred fifty five thousand and twenty five.                   

(b) Indian system: Six crore thirty nine lakh fifty five thousand and twenty five. International system: Six billion four million nine hundred fifty five thousandand twenty five.                       

(c) Indian system: Six arab forty crore thirty nine lakh fifty five thousand and twenty five. International system: Six billion four hundred three millionnine hundred fifty five thousand and twenty five.

(d) All of these

(e) None of these  

Answer: (c)

Explanation

Indian system: Six arab forty crore thirty nine lakh fifty five thousand and twenty five. International system: Six billion four hundred three million nine hundred fifty five thousand and twenty five.