International System of Numeration

Place Value Chart according to the International System of Numeration.


In International system we start grouping the number from right in group of 3, called period and we put comma or space after each period to make the number easily readable.

Reading number according to International System of Numeration

 In International System of Numeration periods such as ones, thousands, millions, billions etc. are used so that number can be easily read.

Let’s read the below number according to International System of Numeration

Example: 115,408,453

First put the number in their respective places.


This number is read as one hundred fifteen million four hundred eight thousand four hundred fifty three.

Marking periods according to International System of Numeration

  • Different periods like ones, thousands, millions and billions are separated by comma (,) starting from the right to differentiate the periods.
  • We start with the first period, named as ones period, consist the first three digits of the given number.
  •  The second period (i.e. thousands period) is consist of the next three digits of the given number.
  • The third period (i.e. millions period), consist of the next three digits of the given number.
  • The fourth period (i.e. billions period), consist of the next three digits of the given number.
Let’s differentiate periods by placing commas in between.

Example: 457833228


This number is separated by comma as 457,833,228

Place Value and Face Value

  • Place Value of a digit is the value of the digit depending on it's position in the number.
  • Place value of a digit is obtained by multiplying the face value of the digit with its corresponding value of the place in that number.
  • Face Value of the digit is the digit itself.
Example: 884,511,009

Expanded Form and Standard Form

When each digit of a given number is written with its place value, then the number is written as the sum of place value of each digit in the number. Then we get the expanded form of that number.
Example: 341,697,832

We can expand any given number in three ways:
  • 3 hundred million + 4 ten million + 1 million + 6 hundred thousand + 9 ten thousand + 7 thousand + 8 hundred + 3 ten + 2 one
Or
  • 3 x 100,000,000 + 4 x 10,000,000 + 1 x 1,000,000 + 6 x 100,000 + 9 x 10,000 + 7 x 1,000 + 8 x 100 + 3 x 10 + 2 x 1
Or
  • 300,000,000 + 40,000,000 + 1,000,000 + 600,000 + 90,000 + 7,000 + 800 + 30 + 2

Successor and Predecessor

  • To find the successor of a given number, we add 1 to the number.
  • To find predecessor of a given number, we subtract 1 from  the number.
Example:
  • Successor of 9,999,999 is
 9,999,999 + 1 = 10,000,000
  • Predecessor of 40,000,000 is
40,000,000 – 1 = 39,999,999

Ascending order

The arrangement of numbers from the smallest to the greatest is called ascending order. This is also called as increasing order.
Example: 8,888,870 < 75,434,108 < 676,576,676 < 677,678,676

Descending order

The arrangement of numbers from the greatest to the smallest is called descending order. This is also called as decreasing order.
Example: 677,678,676 > 676,576,676 > 75,434,108 > 8,888,870

Practice Exercise

QA) Write the number names according to the International System of Numeration.
  1. 13,567,234 - ______________________________________________
  2. 410,015,000 - _____________________________________________
  3. 61,000,030 - ______________________________________________
  4. 750,011,045 - _____________________________________________
QB) Write the numeral according to the International System of Numeration.
  1. Four million, two hundred and thirty-two thousand, four hundred and sixteen._________________
  2. Twenty-five million, three hundred and twelve thousand, four hundred and twenty-two. __________________
  3. Three hundred and fifteen million, one hundred and twenty-one thousand, eight hundred and ten. ___________________
  4. Three hundred and twenty-five thousand, four hundred and two. ________
QC) Write in numerals in words.
  1. The largest 8 digit number. ________________________
  2. The smallest 7 digit number.________________________
QD) Write the place value and face value of the digits 3 and 4.
  1. 13,569,214 - ______________________________________________
  2. 110,015,003 - _____________________________________________
  3. 54,000,030 - ______________________________________________
  4. 390,011,041 - _____________________________________________
QE) Write in expanded form.
  1. 10,026,176 : ____________________________________________________________
  2. 523,406,789 : ___________________________________________________________
QF) Write in short form (standard form).
  1. 2 hundred million + 8 ten million + 4 million + 6 hundred thousand + 9 ten thousand + 7 thousand + 7 hundred + 3 ten + 9 one = _______________
  2. 500,000,000 + 20,000,000 + 3,000,000 + 500,000 + 90,000 + 2,000 + 600 + 10 + 1 = ___________________
  3. 8 x 100,000,000 + 1 x 10,000,000 + 9 x 1,000,000 + 3 x 100,000 + 9 x 10,000 + 4 x 1,000 + 8 x 100 + 3 x 10 + 2 x 1 = ____________________
QG) Write the numeral in figures.
  1. 10 million more than 341,697, 832 ________________________
  2. 20 thousand less than 41,667, 502 ________________________
  3. 1 million more than 4,500,111 ________________________
QH) Write the place value of underlined digits.
  1. 19,527,813 - ______________________________________________
  2. 310,018,003 - _______________________________________________
  3. 14,000,030 - ______________________________________________
  4. 350,011,025 - ______________________________________________
QI) Write in ascending order.

        1)502,389,800; 504,217,450; 481,424,112; 570,000,321
____________________________________________________________
        2)20,000,000; 41,000,000; 40,500,400; 50,525,555
____________________________________________________________

QJ) Write in descending order.

    1) 91,520,704; 91,822,709; 81,245,700; 91,723,714
____________________________________________________________

    2)765,030,000; 89,999,999; 89,999,111; 356,020,900
________________________________________________________

QK) Write greatest and smallest possible number using given digits without repeating the digits.
  1. 2, 0, 1, 7, 8, 4, 9 __________________ ___________________
  2. 3, 0, 1, 5, 8, 4, 9 __________________ ___________________
QL) Complete the series.

501,210,190; 511,210,190; 521,210,190;
________________